"Long-Chain Charlie"
"Shackles & Chains"
"Green, Green, Grass of Home"
"You Are My Sunshine"

Steve Earle's "Over Yonder" and "Ellis Unit One", if you want something modern

"Harrison Town" & "Little Sadie" aren't actually prison songs but a good part of them deals with trial and sentencing.

right now I'm listening to "Deux-Pas des Condamnes" ("Convicts' Two-Step"; recording is Bring it on Down by the Red Stick Ramblers, who are a load of fun. Cajun/swing/old-fashioned jazz).

I've also got "La Valse Criminelle" in my office computer; I think it's the Lost Bayou Ramblers' version.

The Texas River of Song CD is a really cool recording. We got it for my dad for Christmas a couple of years ago--it's not soothing stuff but very interesting