There's not much to the McMichen and Puckett lyrics - probably Riley was taking note of his conscience as indicated in the opening remarks:

Dog eat a catfish, dog eat a minnow
Dog eat a catfish big enough for dinner Dog in the rye patch, dog in the holler
Bring him here little boy, give you half a dollar

In his notes to Rounder LP 1005 'Gid Tanner and His Skillet Lickers', Mark Wilson noted that it was known by both northern and southern fiddlers as 'Ryestraw' or 'Old Ryefields' and other titles. Tunes like this, such as 'Old Mollie Hare' or 'Black-eyed Susan', carried scatological stanzas, but unfortunately Wilson quotes only one:

Dog shit a ryestraw
Dog shit a fiddlebow
Dog tore his asshole
Trying to shit a grubbing hoe

The Fiddler's Companion site gives some others as follows:

Dog shit a rye straw, dog shit a needle
Dog shit a little boy playing on a fiddle

** Dog shit a rye straw, dog shit a minnow
Dog shit a catfish big enough for dinner

** Dog shit a rye straw, dog shit a fiddle bow
Dog shit a little boy working with a grubbing hoe
.
** These lyrics were sung to the "Pigtown Fling" melody by a Michigan fiddler (via Paul Gifford), but are clearly a variation of the above

** Dog shit a rye straw, dog shit a riddle-o
Dog shirt a rye straw longer than a fiddle bow

** Dog shit a catfish longer than a minner-o
Dog shit a catfish big enough for dinner-o

**

--Stewie.