Two Convicts

This appears to be the song referred to in the initial posting, it was recorded in Arvin, California, in 1941, and it can be found on Voices From the Dust Bowl

A song called 'Two Convicts' was mentioned in this article
in Musical Traditions magazine, but I don't know if it's the same song.

The guest who asked about this song mentioned hearing it in Missouri, which would be consistent with the population sources of the 'Okie' migration of the 1930s.