I wouldn't know how to find it, suspect I'd like it a lot. Closest I've come is "Dear Old Donegal" which is probably much later. Also "Peg O' My Heart," which I think is from the 30's. Maybe more, but can't identify it.

I believe the song "There Goes Muldoon, He's an Honest Man" (close as I can come to a title) is Irish-American from the late 1800's although it was collected in Ireland. However I always have to add that I have a memory that often plays tricks on me.... It's a wonderful song anyway, a political campaign song to the tune of "I'll Lay Ye Doon." Trad (more or less), not Tin Pan Alley.

More titles please?