I crosslinked to the lyrics in the Digital Tradition, and to the other thread on this song. I didn't find much source information for the song itself. There's no entry in the Traditional Ballad Index, and only this short mention at folktrax.org:

CLIFFS OF DOONEEN, THE - "I've travelled so far from my native
home" "Far away o'er the mountains far away o'er the foam"
mentions view across the Shannon towards coast of Clare, Kilnarush, Kilkee -
ROUD#9236 -- Mrs Eileen SHERIDAN, rec by Seamus Ennis, London 1956: (RPL
LP 22363) - Irish traveller: LYRICHORD LL-178 1967 (3 v) "C of Duneen"
- BARNBRACK Irish Party Sing-Song: CASS-60-0927 "C of Dooneen"

This seems like a fairly recent song, and it seems we should be able to find a source or a name of a songwriter. This Google Search (click) will take you to a number of Websites with lyrics that are more-or-less the same as what you'll find in the Digital Tradition. The Very Best Irish Songs and Ballads (Walton Publishing) has one different word in the first line:

You may travel far, far from your own native home.

The Walton book says Dooneen Point lies six miles north of Ballybunion, County Kerry. The Walton book does not name a source for the song.
-Joe Offer-