Here's one sung by Homer and Jethro that they don't seem to have written or rewritten themselves. I don't think this is a parody of any particular song (but if I'm wrong, and anyone recognizes it, please let me know!) but rather a satire on the whole folk music revival. I think I hear echoes of the Kingston Trio, various bad-man ballads like Tom Dooley, and especially The M.T.A. (Transcribed from the sound file at The Record Lady's All-Time Country Favorites, Real Country Page 32):

CHARLIE CHEATED ON HIS INCOME TAX
(Milton Addington, Dickey Lee, Allen Reynolds)

(Citizens, listen: I tell you, danger lurks all about us. Now here's the story of an ordinary man...)
I've been workin' on the railroad...
(...who fell victim to a governmental structure that he loved but never understood. Listen well. This could have been you.)

Come all you taxpayers and listen to me well.
I've a story that's very sad to tell
'Bout a victim of the system of legislative acts.
They say Charlie cheated on his income tax.

Now Charlie's been a good man 'most all of his life.
He never even cheated on his wife. (Oh, no?)
A pillar of society, a credit to his folks,
And he'd die 'fore he'd tell a dirty joke.

Charlie, Charlie, what did you do?
Twenty-nine T-men a-comin' after you.
You must be guilty of an awful crime,
If you're worth so much civil service time.

Well, the trouble really started when he bought an old guitar,
Learned to play it like his fav'rite record star, (Don Bowman!)
And when he made twenty dollars on an amateur show,
He declared it so his Uncle Sam would know.

But the form that used was a ten-twenty sheet.
After five o'clock, that form is obsolete,
And between the hours of ten and twelve, you use a W-2,
But on holidays, you file an L-O-Q.

Charlie, Charlie, waltzed through the town,
Handcuffs on and his head a-hangin' down,
Disgraced and dishonored while friends turned their backs,
Thinkin' Charlie cheated on his income tax.

The judge at the trial said, "I understand your plight.
This time I'm gonna make the sentence light."
Well, Charlie stood and faced the bench and shed a grateful tear
As they led him off with only ninety years.

Charlie, Charlie, victim of our time,
Never even understood the nature of his crime,
A lesson to us all that we never can relax
Lest they call us in for cheatin' on our income tax.

I've been workin' on the railroad all the livelong day...