According to the Imternet Movie Data Base these are the songs from the movie, made in 1948. Dean Stockwell plays a character whose name was Peter Frye.
"NATURE BOY"
Written by Eden Ahbez
Sung behind credits by chorus
"TREAD ON THE TAIL OF ME COAT"
Folk song
Sung by Pat O'Brien and Walter Catlett
"HOW MANY MILES TO DUBLIN TOWN?"
Folk song
Sung by Pat O'Brien and boys