Dang!
It seems to happen quite often that I'll search for a song for days, only to find I have it right here at home. I found a wonderful recording of a female version of "Fall on my Knees" on a CD called Stay Awhile, by Jody Stecher and Kate Brislin. I had a hard time picking out all the words from Brislin's singing, but I got enough to get me a phrase that led me to a transcription from a Freight Hoppers recording. It's in a bluegrass songbook in PDF format - here (click). You need Adobe Acrobat Reader to read it.
-Joe Offer (e-mail sent)-

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FALL ON MY KNEES
from the Freight Hoppers

Well I fall on my knees,
Beggin' you please,
Come and stay with me, little girl,
Won't you come and stay with me.

Well I'm going down the line, where the sun don't never shine
Gonna skid on that cold ice and snow, little girl
Gonna skid on that cold ice and snow.
refrain

If I had as many dollars as the sands in the sea
Well I'd give it all to you to marry me, little girl
Well I'd give it all to you to marry me.
refrain

Well I wish to the Lord, I'd never been born
or died when I was a baby, little girl
or died when I was a baby .
I never would have kissed your ruby red cheeks,
or eaten that salty gray meat, little girl,
or eaten that salty gray meat.
refrain

You told me one, you told me two,
you told me ten thousand lies, little girl,
you told me ten thousand lies.
You told me more lies than there stars in the sky.
You'll never get to heaven when you die, little girl
you'll never get to heaven when you die.
refrain

Well the longest train I ever saw,
it was 99 coaches long, little girl
it was 99 coaches long.