I was able to assemble this much of the lyrics from various sound samples found online. I couldn't find a complete recording. These lyrics certainly aren't complete, and the verses might not even be consecutive.

Since we put a radio out in the henhouse,
There's more cock-a-doodle in the rooster's crow.
Hens all sing like Bloke an' Nary(?),
Fill their nests with cackleberries,
And they're twice't as big as farmer Brown's, I know. (I know.)
How the handles of the market basket sigh and groan,
And the crank has fallen off the telephone.
When the eggs begin to hatchin',
Ev'ry chicken comes out scratchin'
Since our henhouse has got a radio.

Now that radio we put out in the henhouse
Was the smartest thing we ever did, by Joe.
When they hear "cock-a-doodle,"
The hens all skiddoodle,
Cluckin', "When ya gotta go, ya gotta go."
We was worried as could be; we had a mortgage due.
We thought our farmin' days were nearly through (nearly through).
Our troubles are over; we're....

[cackleberries = eggs]