I used to start my beginners on two chord songs, using Old Blue and Tom Dooley, which you have, and Iko Iko, Dream Baby and Okie from Muskogee, which you don't have, so they could understand the movement from Tonic to Dominant, also made it easy for them to concentrate on the picking and strumming, instead of getting all bogged down worrying about chord changes--

There are a fair number of two chord pop songs(and many, many three chorders) , as well, but most of them are not worth learning, since most of them are second rate re-writes of old songs anyway, and tend to be forgotten quickly--