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".
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.
Yui's parents in K-On, who love to go on romantic trips.
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 and Beato. In spite of all they went through, they're one of the most stable - and adorable - couples in the VN.
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 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.
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 Sage, Vegeta is struck by the realization that he's content with family life like Goku.
Krillin and Android 18 have a long relationship that includes one daughter.
As common and expected for a group of adventurers, Parn is sometimes oblivious to Deedlit's affections (he eventually returns them after coming to terms with his past), and there's no happy ending for Shiris and Orson.
However, when Laylea is freed from being possessed by an evil spirit, Slayn marries her, 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 much problems.
Damn near every married couple in Naruto, of which there are many. 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 ended up dead.
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's author tells us about the Hosts and a few of the other characters' futures at the end of the final volume.
Honey and manga-only Reiko also end up married, and we're told Mori is married with children somewhere down the line.
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.
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 Katekyo 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.
Kirito and Asuna in the first arc of Sword Art Online. Well... kinda. They're only married by the game mechanics, but the emotional commitment is still there. They still plan to get married for real when they escape the game (and are old enough...)
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.