Sorry if this has already been discussed, but I was having a thought about why Remus Lupin wasn't made dual-godfather of Harry as he close friends with Lily and Jame's second closest friend, and it occurred to me that it must have been because the second godparent position was already taken. This seems odd though that she has never been mentioned, weather dead or alive, like, Harry's godfather gets an entire book dedicated to him and his godmother never even gets a mention? It technically is possible to be Petunia, as Lily always thought highly of her even when she was terrible to Lily, but I feel like that would have been something Petunia would have told Harry to guilt trip him into being more loyal to her.
Anyway, just thought I'd list some potential candidates on who she could have been.
Mary Macdonald: she was a Gryffindor who was at Hogwarts the same time as Lily, though possibly not the same year. Lily seemed to know her as she cared deeply when she was attacked. With her and the second possible godmother on this list I do find it odd that no one, including Sirius would never have mentioned her to Harry. As Mary Macdonald we don't know much more about her besides that, but their is a long running theory that when she got married she became Mary Cattermole, and in that case she is unlikely Harry's godmother as she was still alive and well by fall 1997 and I find it impossible to believe she would never have attempted to contact her godson over the 16 years since he was orphaned, especially since 1991 when he reentered the wizarding world.
Marlene McKinnon: Again, little is known about Marlene, all we do know is that she was in the Order with James and Lily, and Lily cried the entire night after she was killed implying they were close. She died after Harry was born so it is possible she could have been Harry's godmother as she was alive for his birth, and her death could partially explain why she was never in Harry's life, but still doesn't make sense that Hagrid, Mad-eye, and especially Sirius would never have mentioned she was his godmother.
Bathilda Bagshot: I think she is the most likely candidate. Lily was still pregnant with Harry when she and James went into hiding, so they had little contact with anyone from when they first went into hiding, all except for Sirius, Peter, and Bathilda. Lily seemed to become quite close to the old woman in the little time she knew her, so it is possible that since she was close to them while they were in hiding that she was made godmother, and this is further possible by the fact that Sirius and the other Order members didn't really know Bathilda all that well, so they could have not known she was his godmother. Still, like Mary it is odd that in the years between 1981 and 1997 she never contacted Harry, she was quite old so probably couldn't have physically gone to see him, but she could have sent an OWL.
There might be more possible godmothers, what do you guys think?