I asked about the words to On A Monday on the Usenet newsgroup rec.music.folk, and got some interesting replies, which you can find in the Google archives here.

If that link doesn't work, search Google groups for the thread, On a Monday: lyrics? origin?

One response gave the lyrics from The Leadbelly Songbook. In another response, Sam Hinton gave his recollection of the way Josh White sang it in the 1940s.