"And now for something completely different." When I heard Sinead O'Connor's Skibbereen, I thought, "I've heard this tune before." Check out "The Battle of Shiloh Hill" (first line, "Come all you valiant soldiers, and a story I will tell"), written by M.B. Smith and published at page 44 of Allan's Lone Star Ballads (1874). Though words only are given, the song was meant to be sung to "The Wandering Sailor." The lyrics were repeated at page 326 of Fagan's Southern War Songs (1890). Irwin Silber evidently dug up the tune of "The Wandering Sailor" to publish with "The Battle of Shiloh Hill" at page 246 of his Songs of the Civil War (1960) (repeated at page 56 of Silber's Soldier Songs and Home Front Ballads of the Civil War (N.Y.: Oak Publications 1964) and Vol. II, page 300 of Jerry Silverman's Folk Song Encyclopedia (N.Y.: Chappell & Co. 1975). Anyway, despite some variations, the Skibbereen tune seems close enough to be a variation of the "The Wandering Sailor." What do you think?
To range further afield, page 38 of Allan's Lone Star Ballads has a song called "The Texas Soldier Boy" (first line "Come all you Texas soldiers, wherever you may be"). Structural similarities lead me to infer that this was meant to be sung the "The Wandering Sailor" as well. However, when Hermes Nye sang it in his Ballads of the Civil War (Folkways FP 5004) he used a different tune entirely (perhaps one he made up?)
Anyway, if you could trace "The Wandering Sailor" to its source, and then trace its descendants, I suspect you'd find that one of them is the tune currently used for Skibbereen.