Hi, twirpster - put [irish lullaby] in square brackets in the blue DigiTrad search box, and the song will come up. The full name of the song is "Too-ra-loo-ra-loo-ral, That's and Irish Lullaby." Words and music were by James Royce Shannon, published in 1913 by M. Witmark & Sons. I'm pretty sure it's the original version in our database - and it has only two verses.
The song was introduced by Chauncy Olcott in the 1913 musical extravaganza Shameen Dhu. It was revived in 1944 by Bing Crosby in the Paramount motion picture musical Going My Way. Crosby's recording sold over a million disks that year. David Ewen says this song was a favorite of President John F. Kennedy.
Source: American Popular Songs: from the Revolutionary War to the Present, David Ewen.
Search for "Irish Lullaby" at the Levy Sheet Music Site (click) and you'll find three different versions of the sheet music (only two available online).
-Joe Offer-