the version posted by Leslie is published (lyrics only) in Seán McMahon,The Poolbeg book of Irish Ballads. Dublin: Poolbeg, 1991 with the following introduction: "Anonymous Known in the nineteenth-century as 'The Pretty Milmaid,' it was used by the wily old playsmith [Dion] Boucicault to ease the dramatic tension in The Coleen Bawn, and emigrated to America to be one of George M Cohan's songs in his Broadway show Little Nelly Kelly."
Joe Offer brought up the Nelly Kelly angle earlier - has anyone found words, tune, and/or recording, sheet music?