I heard one of the family (Joe, I think) say that A.P. was more of a song collector than song writer, so don't assume that because the Carters did a song it they necessarily copyrighted it. From looking at the titles included in "The Carter Family Collection", I suspect that it's a collection of public domain songs that the Carters performed. The ones that were actually written by the Carters (or copyrighted by Peer) may still be unpublished. However, there are lots of songs the Carters played that are public domain, and you can find them in print if you try. For instance, they did of lot of hymns that can be found in old hymnbooks.