Richard and Mary Parker, the parents of Peter Parker (spiderman) were shown to be happily married before their deaths when Peter was a boy. They were both very much in love when they died and were not said to have had any arguments of note.
Dr. Otto Octavius and his wife Rosie Octavius, are also not shown to have any marriage problems or have any arguments and are portrayed as having a happy marriage.
Nick and Nora Charles, in The Thin Man mystery-movies. It's been said theirs was among the very first truly happy marriages depicted by American cinema.
Adam and Eve in Only Lovers Left Alive have been married for centuries. They're still desperately in love with each other, and that love forms the emotional core of the entire movie. One reviewer noted that they "spend most of the movie draped all over each other", a sign of comfortable lovers who have been together for a long time. Others have compared them to Nick and Nora for the way they schmoop all over each other.
Marge and Norm Gunderson in Fargo. When she's woken up in the middle of the night about a triple homicide, he wakes up alongside her, insisting that she at least needs to eat before heading off to work, so he makes her some eggs. Norm also brings her lunch at work while she brings him earthworms for his fishing. At the end of the film, she tells him that she's proud of his achievement of getting one of his paintings on a stamp.
George and Lorraine McFly at the end of Back to the Future once Marty fixed the change he made to their past.
Given Lorraine's rant to Biff in the sequel, she and George had been happily married in that alternate universe as well, before Biff had George murdered. In the third movie, we see that Seamus and Maggie McFly were happily married as well.
Jack and Marilyn Mickler, in Don Juan DeMarco. It gets even better as the title character's example works its magic on Jack's libido.
Alejandro and Elena in The Legend of Zorro for the most part. They do split up for awhile, but that was mostly because Elena was blackmailed into splitting up with him
The parents in A Christmas Story. Not even the legendary "Battle Of The Lamp" can permanently derail them.
Undercover Blues: Despite a few disagreements about, e.g., taking the baby into dangerous situations, Jane and Jefferson Blues are one of the finest examples of Happily Married to be spotted in an action film. Their easy camaraderie is an enjoyable counterpart to the danger they're facing.
Mike and Jackie Flaherty from Win Win. Their relationship can get harried, but it's ultimately a loving and commited one.
Donald and Tim in the Donald Strachey mysteries are this right from the start, and they're adorable. Not that they don't have their problems, particularly with Donald's dangerous and time-consuming line of work, but that's life.
Celia and Johnny in The Help. All Johnny wants from Celia is for her to be happy. He doesn't care that she can't cook, properly take care of their house or that she had multiple miscarriages trying to give him children. Their first scene together where Johnny sneaks behind Celia and pulls her in close establishes their relationship pretty well.
Greg Kinnear and his wife in The Matador are happily married and their relationship is never at stake.
Andy Knightley from The World's End. Or so he claims. He's actually been having major difficulties as of late, although they get resolved by the apocalypse.
In The Brass Teapot John and Alice are truly happy together and very much in love, despite all their financial difficulties.
In Baghban all the couples in the movie, but Taken up to Eleven for Raj and Pooja. Even though they are married for 40 years, they behave like they are a young couple who are madly in love.
The Hunger Games: The Everdeens had a loving marriage prior to Mr. Everdeen's death.
The Finest Hours: The epilogue shows that the marriage between Bernie and Miriam did happen on the planned date, and lasted for 58 years until he died in 2009.
In Suffragette the chemist and her husband have the only happy marriage shown in the entire movie. The husband is the only man shown who is supportive of women's voting rights, and the one time he's against one of her plans is when he's worried that she, due to her already damaged health, won't survive another run-in with the police.