I checked "Welcome Poor Paddy Home" on Harry Fox Agency's songfile.com website. The Website lists the following as "writers": BRIAN PATRICK MC DONAGH, SHANE PATRICK MCALEER, MICHAEL PAUL HOLMES, JOHN JAMES MITCHELL, CATHERINE JORDAN, WILLIAM PAUL KELLY

Harry Fox Agency song code W75011
Publisher: Soundrights Music

Of course, this could be rights to an arrangement and not to the original song, but Harry Fox is usually a pretty good place to start.

Harry Fox also lists a song titled "Welcome Paddy Home," HFA #W61036, by John Murphy, published by Tunecore Digital Music. It was recorded by the Tin Sandwich Band on an album titled By Hook or by Crook.