The tune of this song is the same as NOBODY'S DARLIN' BUT MINE," by Jimmie Davis, recorded in 1934, which you can hear at the Internet Archive.

(Of course, I can't say for certain that Jimmie Davis didn't get the tune from somebody else.)

Recordings of BLACK AND TAN GUN can be heard at Spotify, performed by--

Johnny Flynn
Sean Dunphy & the Hoedowners
Ray McAreavey & Wolfhound
Padraig Mor
Noel Henry's Irish Showband
...and some others