Hi, I'm a current Cub Scout Leader, and Adult Trainer for the Scout Association. We don't formally train people in camp fire songs, although perhaps we should these days. In the UK adult leaders do get trained in a large number of areas, from child protection to activity design and camp fire lighting and its probably a question of time. As Lizabee says you tend to pass on songs you remember, songs you know and songs you 'steal' from other leaders. Certainly cubs (8-11) are pretty receptive to lots of stuff - the classic songs with actions (Father Abraham), pop songs, through to good gory folk ballads (twa corbies, Sir Patrick Spens).
Having said that there are some song books and lists out there. If you are in the UK go to http://www.scoutbase.org.uk/ and enter 'campfire songs' in the search box and a couple of books will come up.
For the US I found this site, although I can't vouch for the quality of all the songs: http://www.scoutsongs.com/
In general, local scout groups are pleased to hear from folk/acoustic musicians who'd like to visit, perform, and demonstrate their instruments/songs......