I could see Aang simply refusing to do it. He took Ozai's firebending away because it was literally the only option he could find that didn't result in taking his life. In this world, bending is a part of a person's nature, be it genetic or spiritual, and I don't even think the Avatar (at least, not Aang's Avatar) has the authority to go around making new benders just because he can.
Not "just because he can." Because he had to
for the survival of his people and the future balance of the entire world. That balance only survives if airbenders survive, and they're a critically endangered breed. With Aang as the only living airbender, the risk of extinction for the whole nation was monumental. Even 71 years later, there are only five living airbenders, and Amon came close to nullifying all of their powers, if not killing them, in one fell swoop. That's simply an unacceptable situation. Anything that could be done to replenish the airbender population was something that had
to be done for the sake of the entire world, because there's no telling what would happen to the world if the balance were permanently lost by the extinction of one nation. Aang had a moral duty to create more airbenders any way he could, whether by spirit-bending them into existence or just by knocking up hundreds of women. Granted, he didn't do the latter, even though he really should have, because this is a kids' show. But that wouldn't have kept him from doing the former, if it were possible. Thus, the most probable conclusion is that he tried it and it failed.