Jim: I did some more research on the matter and found the following in an edition of the Guardian newspaper.

".....it is derived from the words "iar innis", which is Irish (Gaelic) for "western island"; those words became "Eireann" and then "Eire"."

It is just possible that the author of the song could possibly be refering back to its ancient name i.e. "Beautiful Iar Innis". Just a thought.