My grandmother sang this song to me in the 50's. I remember the words as:
Alabama Coon,

I 'm a little Alabama Coon,
And I ain't been born very long;
I remember one big moon;
I remember one sweet song.
When they took me down to the cotton field,
there I rolled and I tumbled in the sun;
While my daddy picked the cotton
My mammy watched me grow,
And this is what she sang to me:

Go to sleep my little picaninny
Brer fox will catch you if you don't
slumber on the bosom of your old mammy jenny
mammy's gonna swat you if you don't
alu, alu, alu alu alu
Underneath the silver southern moon
hush-a-bye rock-a-bye mamma's little baby,
mamma's little Alabama coon.