Richie,

There's not much to the Mainer version, at least on the recording that I have:

ROCK THAT CRADLE LUCY

Rock that cradle, Lucy
Rock it good and long
Rock that cradle, Lucy
Keep that baby warm

Rock that cradle, Lucy
Rock it good and old
Rock that cradle, Lucy
The baby's getting cold

Rock that cradle, Lucy
Don't let that baby cry
Rock that cradle, Lucy
The baby's born [bound] to die

Unfortunately, no recording details are given on the record sleeve.

Source: Transcription from 'Rural Rhythm presents The Legendary J.E. Mainer and His Mountaineers Old Time Mountain Music' Rural Rhythm LP RR-JE 185.

--Stewie.