Steve,
Early sources (or at least *one*... I can't remember offhand how many I've seen) for "Paddy on the Railway" text say it's to be sung to the tune of Cannibal Islands.


Here's the quick example I could dig up:
https://books.google.com/books?id=-DRYAAAAcAAJ&newbks=1&newbks_redir=0&dq=the%20