The only info I have on Christ Child's Lullaby comes from "The Christmas
Revels Songbook". It says that this traditional Hebridean tune was
collected by Marjory Kennedy-Fraser on the isle of Eriskay. The book has 6
verses, translated from the Gaelic by Seamus Ennis. If you'd like, I'll
send them along.
I have another source for info on tunes, but it will take some time to get
an answer from her.