There are none.
However, since the game has a population of gay horny teens, that means you’ll see a lot of gay ships like Zhongli x Childe, Xingqui x Chongyun, Kaeya x Diluc. Also, I see a lot of people ship Ninguang and Beidou. Despite me loving Beidou, this ship makes no sense. It derives from two lines, that revealed about the shared history the two have as working partners and that Beidou beat Ninguang in Chess twice. However, that’s enough for people to flesh them out to be a couple.
All of the aforementioned are horrible ships that make no sense if you have more than 1 brain cell and think about it objectively.
Childe, who nearly destroys all of Liyue and played a major antagonistic role to stop you is now always portrayed as the Dom in this cracked ship. It doesn’t make sense at all since Zhongli is a powerful Archon and has a more plausible potential love interest: Guizhong. This ship exists for no other reason than seeing two hot guys bang each other.
Diluc doesn’t hate Kaeya anymore, but deep down he resents him and part of his existence is trying to destroy the organization that was responsible for his father’s death. Kaeya withheld information from him and because of that, their father died. They might have some moments where they’re friendly, but given their history, that’s not how they really should react to each other.
Chongyun and Xingqui are just homies. I guess you could make some fanfic and make them be gay in your AU. They have only been portrayed as best friends.