The book cited above only quotes this much of the song:

Mary Jane told me this morning, something that made me afraid.
She said I'd have to marry a man or be a lost ole maid.
I'm so worried I don't know what to do.
I've got a secret; I'll tell it to you.
I don't love any man but my daddy,
And he's already married, don't you see?
Oh, if mama hadn't married daddy,
Daddy mighta married me.

The narrator further comments: "Now I don't know if [grandma] made that song up herself or not. All I know is that I never heard it anywhere else in my whole life. If she didn't make it up, it's got to be the oldest song on record."