It's clearly an Irish song if for no other reason than the lyric, "I'd like to find me brother, the one that's in the army. I don't know where he's stationed, in Cork or in Killarney."

I can find these places on a map and they are all in the Southwest of Ireland. So, as far as I'm concerned, that settles it. Certainly it's possible that there are places in Appalachia with the same place names, but it isn't very likely that the song isn't Irish.