As of the time I'm writing this, there's a recording of "Peg-Leg Bandit" (sic) from Smiley Burnette up on YouTube:
https://www.youtube.com/watch?v=1RD9HHj3g-E

Burnette also recorded the earlier "Peg Leg Jack," so the two have obviously been confused over the years.

The lyrics of "Peg-Leg Bandit" are a bit hard to decipher, but here's my best crack at them:

Oh, there once was a bandit from the Van Horn Peak
And a mean-eyed rat was he,
With one good leg, and the other was a peg,
And he lived in a holler tree;
He never came out till the dark of the moon
And his face, it never showed;
You could hear that peg leg [tap-a-tap-tap]
As he came down the road.

He carved out a notch in the gun that he wore
For many a bloody fight;
With a whiskered chin and a snaggletoothed grin
He started out one night;
But little he knew what trouble brewed
Till the shooting had begun
And a sixgun fanned out (tap-a-tap tap)
And started off the fun!

[Third verse repeats the first with minor differences:]
Oh, the bad old bandit from Van Horn Peak
A mean-eyed rat was he,
With one good leg, and the other was a peg,
And he lived in a holler tree;
He never came out till the dark of the moon
And his face, it never showed;
You could hear that peg leg (tap-a-tap-a-tap)
As he came down the road.

By the flashing pistols, Peg-Leg guessed
He had [out too much bail?];
He knew right then he'd reached his end;
He had a Ranger on his trail;
Now Peg-Leg [quickly told the rest not would he?] fall in grace;
He rapped in vain a (tap-a-tap tap)
Outside the pearly gates!

Outside (tap-a-tap-tap! "Lemme in!")
The pearly ("Open up! Open up!")
Gates!