According to AMG, there are at least 2 songs called "Why Should I Cry over You?"

One written by Chester Conn and Ned Miller, copyright 1922, and recorded by Frank Sinatra, Peggy Lee, and others;

And one written and recorded by Adolph Hofner. It appears on the album "South Texas Swing," 1980, Arhoolie #7029, which is a reissue of old 78's mainly from the 1930's and 40's. I assume this is the one you want.

Barnes and Noble has a sound sample from which I was able to transcribe this much:

"…cry over you?
Why should I feel blue?
I wished, I hoped that you'd play fair
But all along you didn't care
So why should I cry over you?"

I couldn't find any more lyrics, though.