GUEST says "An Irish song is one that:

(a) Is written in Ireland, no matter what it is about.

(b) Is written by an 'Irish' person, no matter how many generations removed from Ireland.
   
(c) Is about Ireland, in even the vaguest fashion.
   
(d) Sounds as though it MIGHT be about Ireland."

But he forgot the main one

(e) Is not written in Ireland; is not written by an Irish person; is not about Irland; does not sound as though it MIGHT be about Ireland; but has been recorded by an Irish singer or group (especially the Dubliners).

And a song can acquire a new nationality by adoption - many songs originating elsewhere are now definitely in the Irish tradition. And you can tell people thet Lamorna is about Manchester until you are blue in the face - it is now as Cornish as the Furry Dance.