"Ni Fhelcim Nios Mo Thu a Mhulirnin" (in English "I Won't See You Anymore, My Dear") is an Irish song. The only lyrics I can find are the Irish Gaelic originals and a machine-generated translation which is pretty poor. This is probably the source of the melody that Stephen Foster used for his "Gentle Annie" in the Legacies section.
The only recording I could find is by Eugene O'Donnell on Slow Airs and Set Dances (1978).