Pete

Listening to it again, I reckon you are correct - he is saying 'coons'. In the first 3 lines, I'm now fairly sure he's saying 'full of':

Nashville's full of big hotels
Chattanooga's full of saloons
Knoxville's full of Republicans
And Memphis lots of coons

I am glad my misshearing can be of assistance to you. But you still have the problem of the 'yella gal' verse, unless you simply omit it.

Here's what I can hear of the rest. The third verse is a little different from Clifton53's recollection. I haven't a clue what he is singing in last 2 lines of the last verse. Any ideas?

Wish I had a sugar-o (?)
Sugar by the pound
Great big bowl to stir it in
Pretty girl to hand it around

Big bee sucks the blossom
Little bee makes the honey
Poor man makes the cotton and corn
The rich man sees the money

Master had a yella gal
He brought her from the south
Tied (tight?) so curly on her head
She could not shut her mouth

People on the corner
Watchin' us go by
Could not see ...(a sparrow ?)
....................

--Stewie.