Many, if not most, airlines offer international adoption fares. United & Lufthansa, for example, have some (limited) info on theirs here. No idea if they offer domestic ones, though I suspect not. (Even if they do, I couldn't say how much better the fares are than "off the rack" ones.) Still, it couldn't hurt to call and ask about adoption fares. Definitely don't wait until the last minute to inquire.

If you mention the place from which they're adopting, FTers may be able to suggest some of the better airlines to contact. It would also be good to post the specific date window they're considering, as undoubtedly open tickets would be a better or worse deal depending on exactly when they need to go.

And, last but certainly not least, congratulations to the happy (soon-to-be) parents!