I have been singing the version that Jimmy C shared for many years; I heard it on a Jean Redpath album called simply "Jean Redpath", and she calls it "Ned of the Hill". I will quote her notes on the album cover:

"Although this song has a double entendre, I think of it, and sing it, as a love song. Edmond O'Ryan, in supporting the Stuarts, was outlawed after the defeat of James II, and his estates confiscated. As in other songs, the 'Eileen' spoken of here can also be understood as Ireland herself. Samuel Lover (1797-1868)was the composer of this, and of the better known "LOW-BACKED CAR" AND "RORY O'MORE".