What can I do to repair my headliner instead of replacing it?

If it is coming down (turning loose from the foam backing), there isn't much you can do to repair it without replacing it; although if you don't care that much what it looks like, you can thumb tack it back up or something like that. If it's just coming loose at the edge, (headliner and foam), then you can glue it back up in those spots.

If it's coming down all over, do it right and replace it !