I never thought of "Paddy" as a chantey until I found it in Frederick Pease Harlow, Chantying Aboard American Ships, p139. And why not?

He gives fairly standard verses and then:

        In eighteen hundred and forty-nine,
        I then concluded to resign, (2x)
        From working on the railway,
        
        In eighteen fifty, I soon found,
        Meself shanghaied, for Frisco bound, (2x)
        To work upon the railway,

        The railway started me to roam,
        But the sea is hell and I can't get home, (2x)
        To work upon the railway,