The info below may help you track down the music:

http://www.quietmanmovieclub.com/isleofinnisfree.htm
 
Dick Farrelly and "The Isle Of Innisfree"
- a note by his son, musician, Gerard Farrelly…

. . . "The Isle Of Innisfree" was published in 1950 by Peter Maurice Music Publishing Co. Ltd.  In early 1952 Bing Crosby recorded it and subsequently it became his biggest ever UK hit. John Ford fell in love with the song and was so struck by the beauty and passion of the melody that he decided to use it as the principle musical theme of "The Quiet Man".  "The Isle Of Innisfree" almost totally dominates the sound track of the movie and is used whenever there is intense emotion or feeling.  It is first heard over the opening credits with the majestic Ashford Castle in the background at sunset. 

The song has since appeared in the soundtracks of the films – ET (1982), when a clip from "The Quiet Man" is shown, and "Distance Voices, Still Lives" (1988). "Innisfree" has been recorded by hundreds of artists worldwide – Joe Loss, Vera Lynn, Val Doonican, Joseph Locke, Finbar Furey and Tommy Fleming to name but a few, and endures as one of the most loved Irish songs.
So it was first published 55 years ago.
Good luck.
It is indeed a beautiful song.
I have a friend that was able to find song sheet music online that the website will transpose into any key for you, and you can print it out. I am not sure if this one is in their catalog. It does cost some money for each song.
Richard C. Curry