Correction: the Flanagan Brothers album is called "The Tunes We Like to Play on Paddy's Day." There's a review of it here. It does indeed contain a song called "The Half Crown Song."

Frank Maher posted THE HALF CROWN SONG attributed to Joe Flanagan, 1933, in another thread.

However, it doesn't contain the lines that are quoted above. It seems there are more songs in this family that we haven't collected yet.