You're right, Celtaddict - it's on page 140 of Cole, and the lyrics you posted are almost exactly what's in Cole.
Cole says "Sleep soft, my baby," but I like "bairnie" better. I transcribed the tune from Cole.
One thing, though - I can't find it on Bok's Dear to Our Island. What is the name and number of the track? I do find a track with that name on the Alan Lomax Collection CD, World Library of Folk & Primitive Music (Scotland). I'm confused. I have all of Bok's CD's and can't find this song.
-Joe Offer-