All the "I wouldn't marry verses are widespread from the mainland to the Caribbean, and found in books that include Negro secular song. They are floaters in a number of dance and party songs. The origin is believed to be minstrel (see Ethiopian Serenaders verse, below).
Here are some:

I wouldn't marry a yaller gal,
I'll tell yo' de reason why;
Her hair's so dad-blamed nappy
She'd break all de combs I buy.

I would n't marry a yaller gal,
I'll tell yo' de reason why;
Her neck so long and stringy
I'm 'fraid she'd never die.

Newman L. White, American Negro Folk Songs, 1928, Songs about women # 31. From Walter Jekyll, Jamaican Song and Story, 1907.

I don't like a black gal,
I tell you de reason why;
Her hair so long and kinky
She will break every comb I buy.
etc.
Coll. 1915, Auburn, AL, MS of A. M. Kearly, in White, American Negro Folk Songs.

The Ethiopian Serenaders of the 1850s:
Ole Massa owned a colored girl,
He bought her from the South.
Her hair is curled so very tight
She could not shut her mouth.

From Talley:
I wouldn't marry a black gal
I'll tell you de reason why;
When she goes to comb dat heat
De naps'll 'gin to fly.

I wouldn't marry a black gal,
I'll tell you why I won't:
When she oughter wash her face-
Well, I'll jes say she don't.
etc., etc. With sheet music, p. 49, No. 46, Thomas Talley, Negro Folk Rhymes.

The "Went Out on the Mountain verses also float, and derive from a combination of religious and perhaps minstrel origins.

I went to de ribber, but I didn't go to stay,
But I got so drunk I couldn't get away,
My marster axed me whar I'd been,
And the way he hit me was a sin.
(From White, p. 1332, Upstart Crows no. 1B, coll. 1915.
(Based on the spiritual "I went down to the Valley to Pray)

I went up on the mountain
To see the rising sun;
Ain't found nobody
To treat me like my woman done.
(White, p. 338, No. 81, coll. 1915, Auburn, AL.