Steve Roud's folksong index lists numerous broadside copies, none of which contain a tune direction. I can only find 1 on the Bodley Ballads website (use 'Parker'. other keywords from the 1st line don't work).

Verions with traditional tunes are in Baring-Gould's 'Songs of the West', 1905 edition; JFSS, 1930; and Frank Purslow's 'The Wanton Seed'.