The version sung by John McCormack, and composed by Alicia Adelaide Needham, can be found online at the Traditional Music Archive, at itma.ie as a single piece of sheet music for voice and piano (looks like low or medium voice, too low a key for a tenor like McCormack).

The title is "My Dark Rosaleen", An Irish Patriotic Song, 17th century
The words from the Irish by James Clarence Mangan,
Set to Music by Alicia Adelaide Needham
publication: New York: Boosey & Co., 1897
which makes it in the PUBLIC DOMAIN

Of James Clarence Mangan's seven verses, Ms. Needham set to music verses 1, 3, 4, and 7.