Some of the verses above are similar to those of "Massa Had a Yaller Gal," variants of which have been quoted by White, Odum, Scarborough, Talley and others. These verses have been discussed in other threads.
An article in Literary Digest, 1916, mentions variants from South Carolina, dating back to 1876-1886 (White, American Negro Folk-Songs, p. 152-156).
Examples:

Massa bought a yaller gal,
He bought er frum de south;
Her mouth look like de fireplace
Wid de ashes taken out.

Of all the beasts that roam the woods
I'd rather be a squir'l,
Curl my tail upon my back
And travel all over this worl'.

"Simon Slick" is similar:
Ole marster was a stingy man
And everybody know'd it;
Kept good liquor in his house
And never said here goes it.

Fitting the meter of "It Ain't Gonna Rain No Mo'" much better are songs like "Uncle Ned," a minstrel song from 1848, but the tune is different:

Den lay down de shovel and de hoe,
And hang up de fiddle and de bow;
Dere's no more work for poor Uncle Ned
He's gone where de good old niggers go.
N. I. White; Alabama, "sung by Negro who fought in Civil War," p. 164ff.
(Digression: The above verse was paraphrased in the Ethiopian Serenaders' Own Book, 1857. White found it surviving and sung by a Black in Alabama. One verse:
Then lay down the agricultural implements,
Allow the violin and the bow to be pendent on the wall,-
For there is no more physical energy to be displayed,
By indigent aged Edward,
For he has departed to the abode designated by a kind
Providence for all pious, humane, and benevolent colored individuals. )

I WOULDN'T MARRY
Used by Johnny Carson in "It Ain't ....," some of the verses may go back to the Ethiopian Serenaders of the 1850's. A variant on "Massa Had a Yaller Gal."

I wouldn't marry a yaller gal,
I'll tell you de reason why:
Her hair's so dad-blamed nappy
She'd break all de combs I buy.
Verse from Jamaica (White, p. 323), but little different from those sung in the southern states.

Also common are the white, yaller and black lady-gal comparisons.

Well a white lady wears a hobble skirt,
A yaller gal tries to do the same,
But a poor black gal wears a Mary Jane,
But she's hobbling just the same.

The form goes back to songs that probably originated with Black slaves:
Mr. Coon he is a mighty man,
He carries a bushy tail
He steals old Massa's corn at night,
And husks it in a rail.

All above examples from White, collections of about 1915, but they can be duplicated and added to in the other references mentioned above.