I have a copy of this recording and the lyrics in an old record album of lullabies from 1966. First printing was listed as 1956. It was on the album, Golden Slumbers (A Caedmon Soundbook with high fidelity record). I remember this was one of my favorites growing up and I was so surprised that I found it again. This book has lullabies from all around the world with simple sheet music and lyrics listed. This one is on page 19. It was recorded by Robin Roberts who said she was taught the song along with the one titled "Dance to Your Daddy," by Mrs. Elizabeth Cronin.
The Irish lyrics listed here are : "Purteen hyann a teetha 'ss inneen fillib a chyeoil."
Hope this helps someone else out there. I wish I could find this version on Cd, it would make my year!