Following Jabbajahda's suggestion, I found some which seem close:

https://www.loc.gov/resource/ihas.100007715.0/?sp=1

It's a City of Sighs and Tears, it's describing a girl who goes away. Though we'll probably never know for certain, this seems close.

To boot, there are a few recordings old enough to have existed back then:

Robert Price singing

J. W. Myers' recording - estimated to have peaked at #4 song at the time