I don't know when this joke was made up, but I first heard it when I was in high school, and I graduated in 19 and 57. When we used to tell/sing this joke Rose was Sue and the line was a bit sorter (ten words...it is a telegram after all).

Knock on the door...woman opens.
Man in cap and uniform says, "Telegram for Mary Smith".
She gushes, "Oh goody, a singing telegram!"
"No lady, this is just a regular telegram. I hand it to you and you give me a tip."
"Oh, please sing it to me. I've never had a singing telegram."
"Lady, you don't understand. This ain't no singing telegram."
"Please, please sing it."
Exasperated, "O.K., Lady." Tears open the envelope and unfolds the page,and sings, "Da da da da da da 'sister sue is dead you know she died in bed'"