Baucis and Philemon. Having entertained Zeus and Hermes unaware, they received having a wish granted. They wished that they would die at the same moment so that neither of them would have to live widowed. They didn't even die exactly; at the end of their long lives, as they stood looking at one another, they were transformed into a pair of trees with the limbs intertwined so that they could never be separated.
Odysseus and Penelope from The Odyssey. Okay, there was the stuff with Circe and Calypso but neither of those was what you could call "voluntary" and he did go to the ends of Earth (and Hell, and back) to get back to Penelope. That counts for something. For her part, Penelope did all she could to hold off the obnoxious suitors and stay faithful to her husband.
Eros and his wife Psyche are an unlikely pair, considering how the vast majority of the Greek pantheon was constitutionally incapable of anything resembling fidelity. The story of the origins of their marriage is about trusting and going to great lengths to mend bridges.
The Rescue Romance of Perseus and Andromeda. Just the fact that neither cheated on the other is a very good sign.
Hilariously, TyphonandEchidna. Two of the worst monsters to ever come out of Tartarus (who by the by is their father), are entirely faithful to one another and support each other in all of their endeavours. Typhon eventually becomes Sealed Evil in a Can, but Echidna never moves on, and all of her young (and there are a lot of them) are also Typhon's. By Greek standards that is weirdly functional.
Hector and Andromache in The Iliad in sharp contrast to everyone else. Priam's a philandering bastard, Helen and Menelaus/Helen and Paris are horribly dysfunctional, and we won't even get started on Agamemnon and Clytemnestra. Hector and Andromache honestly seem to have been a good match.
Orpheus and Eurydice until she was dragged to Hades and even then, he loves her so much that he goes to Hades and back to try and get her back.
Hades and Persephone. Hades cheated on her once in the three thousand years they've been together (and that's only if you read one, lesser known myth), and the fact that he wanted to marry her (as in, keep her around) rather than have a one-night stand speaks volumes in Greek mythology. In some versions of the aforementioned lesser-known myth, the woman in question is actually his ex rather than a mistress.
Cyane and Anapos. Cyane tried to stop Hades from abducting Persephone by citing her own happy marriage as an example of consensual relationship, and as the opposite of Hades' own methods.
Freyr and Geršr, though getting her to fall for him leads to his death he didn't regret it.
Balder and Nanna. The Norse really liked their gods to be happily married before they were killed by giants.
Egyptian Mythology has Osirus and Isis who were surprisingly non-dysfunctional considering they were siblings. When the former was killed, the latter devoted much of her life to bringing him back.
Robin Hood and Maid Marian didn't get married in many of the original ballads (usually because she didn't exist yet), but many adaptations happily pair them off. The commentary for the 2010 movie stated that each era makes them into that era's idea of the perfect marriage.