I see that some playlists from The Dr. Demento Show include a song called "Are You Lonesome Tonight? (laughing version) - Elvis Presley." I don't think I've heard this one, but I presume it's some sort of outtake in which he broke up during a recording session.

In a similar vein, a local radio station has played a recording of Rudy Vallee singing "There is a Tavern in the Town" in which he totally breaks up into hysterics halfway through. What prompts the breakup is that when he comes to the lines

Adieu, adieu, kind friends, adieu (yes, adieu)
I can no longer stay with you (stay with you)

he first pronounces "adieu" in the authentic French way, and then, inadvertently I presume, he pronounces "you" to rhyme with it EXACTLY. Then he realizes how silly this sounds, and starts to laugh, but then he tries to struggle through the rest of the song! It was hilarious to listen to.

By the way, I did find some confirmation that Homer & Jethro recorded "Are You Lonesome Tonight" b/w "I Love Your Pizza" as a 45-rpm record, RCA #101030, or maybe RCA #4/60233, depending on which web site you believe. No other info, though.