I got the Cool Hand Luke DVD and the original soundtrack recording (Oscar nominated score by Lalo Schifrin) by Aleph records. I would recommend the DVD over the CD for the music, especially for Plastic Jesus. The DVD has the banjo instrumental and Newman's song. The CD is all instrumental. The DVD was $14.27 and the CD was $13.38 from Barnes and Noble.
I recommend the DVD as a very good movie. My favorite scenes are:

Requiem on the banjo (Plastic Jesus sung by Newman)

The lady washes her car (with "Lucille", the hot Joy Harmon)

Into The box (the beautiful banjo instrumental by Tommy Tedesco)

From the link that Stephen Farris gave in thread above and from the Smithsonian Folkways site:

Ernie Marrs arranged his version of a song [Plastic Jesus] that was already in circulation, although it was frequently credited to him. Actually, it was written by two West Coast musicians, Ed Rush and George Cromarty, who were members of the Goldcast Singers. Ed Rush traced the song back to an African-American camp-meeting song with lyrics "I don't care if it rains or freezes, leaning on the arms of my Jesus," which was the theme song of a religious radio program broadcast from Baton Rouge in the 1940's (Broadside # 41).

The banjo credits go to Tommy Tedesco {Quote} billed as "the most recorded guitarist in history," was certainly one of the top session guitarists of all time, able to play convincingly in virtually every style of music, but concentrating on pop/rock, jazz, and soundtrack work {End Quote}

Cruiser