Shintarou and Sakura, Ichigo's parents in Tokyo Mew Mew, are an overdramatic pair that acts exactly like newlyweds. One is an Overprotective Dad and the other approves of anyone Ichigo brings home, but otherwise, they agree on absolutely everything. Ichigo mentions that they're her "ideal couple".
Near the end of Hakoiri Devil Princess, it is revealed that Maki and Keita are happily married and live a peaceful life together forever after the hardships that they've endured.
Both sets of parents in Marmalade Boy. Even with the issue of having swapped partners and then moved into the same household all of a sudden, and from then on they're shown to be very in love with their new partners as well as friendly between the four. It's a Justified Trope, in the end: The four have actually been friends for atleast twenty years, and back then the 'couples' were swapped as well.
In the beginning of D.N.Angel, it appears as though Daisuke's father is either dead or deadbeat, since he isn't around and is never mentioned. Soon, however, Kosuke comes back home from researching something related to the Niwa family history, and it turns out he and Emiko are very much in love and a shining example of this trope.
Miu's parents from Piano bicker somewhat from time to time—especially about him drinking—but their marriage is usually very harmonic.
Hohenheim and Trisha, despite the fact that they weren't married. When Hohenheim left (because he didn't want to watch as his family aged and died), Trisha waited for him to return and remembered him fondly. It's implied that she knew he was immortal and still loved him, and a manga omake has them Together in Death.
King Bradley and Mrs. Bradley. Admittedly they had a pretty rocky start, according to Mrs. Bradley, but they are very close and loving and genuinely Good Parents to their adopted son Selim. Although it's part of his cover, the fact was that King Bradley chose her to be his wife unlike how everything was decided. It was a rare moment of true humanity for him.
In the ending of the manga, one of the final panels shows a picture of Edward and Winry being happy together in what is a new Elric family photo while holding their children. Also notably in the picture is Alphonse and May being present, heavily implying that May did end up marrying Alphonse. The Brotherhood adapation expanded the family photo to include Paninya and Winry's automail mentor.
The parents of Yukino Miyazawa and of Soichiro Arima in Kare Kano are all happily married, despite Hiroyuki Miyazawa (Yukino's father) not getting on with his father-in-law, and despite the problems with Soichiro's real parents (he's living with adoptive parents, who are the happily married ones). By the end, Yukino and Soichiro themselves.
Togusa and his wife (and their children) in Ghost in the Shell: Stand Alone Complex, though we only get the occasional glimpse of his family in the show; Solid State Society uses them a bit more, eventually leading to arguably the most painfully suspenseful moment in the movie where Togusa is forced to choose between letting the Puppeteer force him into giving up his daughter for brainwashing while cyberhacking him, or killing himself to let her go free. He chose suicide and, if it wasn't for the Major, would have gone ahead with it.
After EP6 Battler is this with Beatrice, of all people! In spite of all they went through, they're one of the most stable - and adorable - couples in the VN.
Rich Bitch Eva and Nice Guy Hideyoshi. They're specially noted to be very happy in their marriage despite Eva's big problems with the rest of her Big, Screwed-Up Family. Even worse — they're so happy and love each other so much that, whenever Hideyoshi bites it in the time loops... Eva completely snaps.
In Yu-Gi-Oh! ZEXAL, Yuma is unique in the franchise in that he is the only protagonist with both parents known (or at least presumed) to be alive; they are currently missing, but in flashbacks there was never any sign of discord between them.
This caused problems in the backstory of Mahou Sensei Negima!. Negi's father, Nagi, was Happily Married to Negi's mother Princess Arika when he met Evangeline- and, naturally, he wouldn't respond to her advances because he was perfectly satisfied with his wife. In the end, he had to seal Eva in a boarding school just to get her off his back.
Also, Yuna Akashi's parents were all but stated to having been this in the past. At least until Yuna's Missing Mom, Yuuko, died in the war. Mr. Akashi has never remarried and still remembers Yuuko very fondly.
It began as a brief fling and then they didn't give a crap about each other for awhile, but Vegeta and Bulma eventually became this in the latter parts of Dragon Ball Z. During the Buu Saga, Vegeta is surprised to be struck by the realization that he's content with family life like Goku. It's made more apparent in Dragonball Super, particularly in scenes with their children (Trunks, Bra, even Future Trunks). Even if they hate to admit it outright most of the time.
Krillin and Android 18 have a long relationship that includes one daughter.
The short story Dragon Ball Minus reveals that Goku's parents, Bardock and Gine, were this. According to Word of God, this was highly unusual among Saiyans, as most pairings were done simply for breeding purposes.
Axis Powers Hetalia offers a ragher cute subversion with Austria and Hungary. They are pretty happy together — but technically speaking, they're divorced after the disolution of the Austro-Hungarian Empire, which in Hetalia-terms equals to their marriage.
Karin gives us Karin's parents, Carrera and Henry, who pull this despite Henry being kind of a Henpecked Husband and Carrera being a tsundere. The affection still runs pretty deep. The epilogue shows us Karin and Kenta themselves — seven years have passed and they're pretty happy in their marriage, which includes a Daddy's Girl daughter named Kanon.
Kyoko and Katsuya Honda from Fruits Basket were this trope for the brief time they were both alive at the same time. Specially meaningful because Kyouko comes from an abusive household and Katsuya came to ask for her hand in marriage (she was still a minor)... when her parents were about to disown her. Katsuya stepped in, told them off and took Kyoko in, which allowed her to re-start all over and finally have a happy life.. Also, Kyo and Tohru Sohma and most likey every other Official Couple.
Record of Lodoss War: When the priestess Laylea is freed from being possessed by an evil spirit, she marries the mage Slayn. They have a daughter named Neese, and their relationship continues without any problems.
In Hayate the Combat Butler the parents are either missing (and it's usually hinted that they're just happily married behind the scenes), unseen or Happily Married. There seems to be no middle ground between these three. Even Hayate's parents are portrayed as Happily Married.
Though we haven't actually seen Mr. Katsura, between Hinagiku's happy life as their adopted daughter and Mrs. Katsura's outlook, they are probably the happiest.
Wilhelm and Dorothea Malders from Victorian Romance Emma, one of few noble marriages shown to be happy and without many problems.
Damn near every married couple in Naruto is happy, of which there are many. This ties in with the themes of family and bonds, but also makes up for the fact that half the cast are orphans and those same happily married couples quite often end up dead.
This is also played straight in the epilogue onward; Naruto and Hinata, Sasuke and Sakura, Shikamaru and Temari, Sai and Ino, and Chouji and Karui get to have their happy endings as married couples, which we see more of in the sequel series.
The majority of the One Piececouples are these, even if one of the spouses (usually the mother) is deceased. One example is Queen Otohime and King Nepture in the Fish-Man Island arc. He is a strong supporter in her determination to bring humans and mermen together. In a subtle but very sweet scene, Queen Otohime before going with the World Noble to negotiate reassures King Nepture to trust in her as his wife. It's perhaps the series' first, and probably only, if Eichiro Oda has anything to say about it, unambiguously romantic scene.
Ouran High School Host Club': It's implied that Haruhi's parents were this until her mother's death prior to the start of the series. In fact, her father says he was so in love with her mother that after she died he could no longer be attracted to women.
Black Butler has Ciel's, now deceased, parents. In life it appeared that they were happy together and Good Parents. At least, it did in the anime, and in the manga from Ciel's point of view. Vincent's conversations in the Baron Kelvin flashback chapters beg to differ.
Windaria Alan is so happily married that thoughts of his wife can repel evil spirits.
In The Familiar of Zero Saito and Louise get married at the end of the final season, overcoming both Saito's perversion and Louise's tsundere nature and the many, many obstacles in their way to doing so. Then the newlywed couple opens a portal to spend their honeymoon in Saito's world and introduce Louise to Saito's parents, overcoming one of the big issues with their originating from seperate worlds.
Mobile Suit Gundam 00's Patrick Colasour and Kati Mannequin get married at the end of the series, and two years later in The Movie are shown to be very happy together, although she's exasperated by his inability to call her anything other than "Colonel" (her actual rank at that point is a General).
Iemitsu and Nana from Katekyō Hitman Reborn! fit this trope well. They're as lovey-dovey with each other as they were when they were younger, and Iemitsu's "mysterious" goodbye to her right before leaving for a few years makes her swoon even years later.
Sword Art Online: Kirito and Asuna marry during the first arc. It's only according to the game mechanics, but the emotional commitment is still there. They plan to get married for real when they escape the game (and are old enough...)
In Half Prince, Lan ends up happily married to Gui, despite her considerable issues in originally accepting her femininity.
Haruto and Yuzuki are happily married in the final manga chapter of Kimi no Iru Machi.
Sachiare! is about a blissful young couple... um, well, being blissful.
Inuyasha and Kagome happily marry after the latter's mother gave her blessing to go back time to the Sengoku era to live with Inu for the rest of her life.
By that point Sango and Miroku's formerly rocky relationship has stabilized well enough for them to have three children (one of them being a newborn at the end) and spend their life in a mostly happy environment.
Usagi and Mamoru happily marry in the future and they will become parents of a daughter named Chibiusa, but we see little of that time.
Similaly, Usagi's parents Kenji and Ikuko are shown to be a very stable couple and very affectionate to each other and their kids.
Keiichi and Belldandy go from a sweetly engaged couple to an equally sweet and secure married couple at the end of Ah! My Goddess.
Mahiro's parents in Haiyore! Nyarko-san, who are in the middle of their seventeenth honeymoon at the start of the story; note that this means they've averaged one honeymoon a year since their son was born. When Mahiro finds out that his mother is a part-time monster hunter and god slayer, he asks if Dad knows; Yoriko says of course he does, then blushes like a schoolgirl while saying that his being so supportive and understanding is part of the reason she loves him so much. (For the record, Dad is The Ghost, stuck at the office making up for the time he took off for the latest honeymoon and never shows up in the novels.)
Surprisingly enough, Nile Dawk from Attack on Titan turns out to be this. Though the commander of the infamously corrupt Military Police Brigade, it turns out he's actually happily married and a proud father with two children and a third on the way. His former classmate, Erwin Smith, praises him for being able to achieve the happiness so many of their comrades nevercould.
In Tonari no Kashiwagi-san Kotori and Takuya have been a couple since their school years, and still manage to have their cute moments.
Kyouko and her husband from Okusan still act like newlyweds and have a very active sex life despite being married for six years. This comes as a shock to Kyouko's housewife friends who are jaded when it comes to their marriages.
Kaoru and Hajime in I Can't Understand What My Husband Is Saying. Despite one of them being an Otaku and the other being normal, they are still incredibly close. They are shown to have an active sex life, and the worst argument they ever have is deciding what their daughter's name should be.
When Katarina Claes reincarnated as a noble in Destruction Flag Otome, her parents had a slightly strained relationship due to a misunderstanding about their arranged marriage. It is further complicated when her father adopted a distant relative because his heir and daughter was engaged to royalty and thus couldn't inherit the family name. But thanks to Katarina being more rambunctious than she was supposed to be, she causes a small incident that clears up both their concerns about having forced their partner into the marriage and duchess Claes' misunderstanding that her husband had cheated on her and produced a son. Afterwards they're said to be very happy and affectionate towards each other.