Mrs. Zezam, I think the song you're after is from the old Irish film "Peg O' My Heart" (1933) and it's called "Sweetheart Darlin'. I'm not 100% that it's the right one as I can't find the lyrics but it is on this album
click here
Also sung by a man called Morton Downey.
click here too!
Good luck with your search,
best wishes, Yvonne