Richard Burnett's Man of Constant Sorrow, 1913, is in Richie's post to thread 35233 (East Virginia thread): East VA
Also see Farewell

Much information in Mudcat. Try- i am a man, constant, sorrow, farewell, etc., in both filter (for about 180 days) and in Supersearch.
Also see thread 25469 O Brother where Stewie discusses the Farewell Song (Man of constant...). Whether the traditional tune in the song is English, Irish, Scots or North American is, I believe, open to question.