Fire Emblem is a RPG series that has been around since 1990. Recently it has garnered attention since the release of Fire Emblem: Awakening, which actually financially saved the game series.
While Fire Emblem: Awakening did not have same-sex marriage in it, there were hints of bisexuality. Specifically with one character named Tharja.
Tharja is a dark mage player character that is known for her evil nature and love for hexing. She has an incredibly unhealthy obsession with Robin (the Avatar character that the player, plays as, which can be either male or female). This obsession is outwardly presented as romantic, and she is very open about her adoration for Robin. Robin on the other hand, is creeped out by her at first. Although, if the player were to progress their support conversations together, Robin eventually learns to trust Tharja and actually enjoy her presence. And if Robin is male, he can marry her. However, the female Robin’s support conversations are almost identical to the male Robin’s support conversations with Tharja. The only big difference is that Tharja can only marry the male. And while this is heterosexist, the reason behind it is most likely because the game is set up that the children of the player characters come from the future to help their parents in the war. Female player characters have set children, which will obtain the qualities of the father that the female marries. So, Tharja’s daughter, Noire, has stats determined by whoever Tharja married (because they will be Noire’s father). As such, if Tharja were to marry a woman, Noire wouldn’t have a father, and thus wouldn’t be able to be born (or even created in the game unless they used her default stats).
So, unfortunately this game doesn’t include a canon homosexual couple. However, it is likely that there will be the potential for one in the near future. The “children mechanic” of this game, is individual to this game in the franchise. Meaning that it is unlikely that they will continue with the child mechanic, so in the future, there will probably be the opportunity for a nicely portrayed homosexual couple, since it won’t mess with the gameplay. And hopefully it will be with characters a little less evil than Tharja (and don’t follow into the “murderous queer” trope).