There is a long entry, with lyrics, at Ceolas, The Fiddler's Companion (in combined article with "Cacklin' Hen," scroll down). Some stray verses:

CLUCK OLD HEN

Cluck old hen, cluck for your corn,
Cluck old hen, your winter's all gone.

I had a little hen, she had a wooden leg,
The best danged hen that ever laid eggs.

Lair more eggs than the hens around the barn,
Another little drink wouldn't do me no harm (Tommy Jarrell)

Cluck old hen, cluck all night,
Soon you will be Chicken Delight.

Possible, possible, my fat hen.
She lays eggs in the relative when.
She might lay eggs in the positive now,
If only she could postulate how.

Possible, probable, my black hen
She lays eggs in the relative when
She can't lay eggs in the positive now
For she's unable to postulate how (Spark gap Wonder Boys)

Cluck old hen, cluck I tell you,
Don't lay an egg, I'm a-gonna sell you (Joel Shimberg)

My old hen died, what'll I do,
Guess I'll have some chicken stew. (Neal Walters)

Cluck old hen, cluck I say,
The Dow-Jones average is down today.
Cluck old hen, cluck six-ten,
The Dow-Jones average is down again. (Neil Rossi)

The old hen she cackled,
She cackled in the morn;
She cackled for the rooster
To come get his pecker warm (Tom P. Smith, West VA.)

and others.