This might be a bit of a reach for this site, but others might have better luck than me at researching this.
The song "Goodbye My Coney Island Baby" shares a melody with the "war hymn" (fight song) of Texas A&M University, known as "Aggie War Hymn".
I'm unable to figure out which came first though. The college fight song dates back to 1918 (though it wasn't officially introduced until a couple of years later), while Wikipedia says "Goodbye My Coney Island Baby" was composed in 1924.
While it seems unlikely that a song would be written about a girl in New York to the tune of a college fight song from a school in Texas, I guess anything is possible. What's even more confusing is that Wikipedia's composition date for "Coney Island Baby" doesn't make sense as 78discography lists a recording on the OKeh label from 1922.