I was curious about this a year or two back, and did an Internet search for "Dooneen". If I remember right I did find one in Co. Kerry, but on the Dingle Peninsula, which would be a good few miles south of Ballybunion. A recent web search gives a poem below which indicates there is a Dooneen on the Dingle Peninsula (relevant verse below).

The softly spoken Gaelic, tales of ships that sailed from Spain,
The ancient Church at Gallarus and Fuchia in the rain,
A school of glistening black canoes stranded at Dooneen,
And Brendan's Voyage from Brandon Creek for paradise unseen

My 1:5000 Irish Ordnance Survey Map No. 70 shows a "Dooneen Pier" at Grid Reference Q390092 in a west facing inlet on the north coast of the Dingle Peninsula, about a mile from Ballydavid and several miles along the coast from the above-mentioned Brandon Creek. The map does not show steep contours here so any cliffs if present are likely to be low.

As I have not been at the spot I cannot say whether one could see Kilkee and Kilrush, though this is perhaps possible. As far as I know there are cliffs on the Dingle Peninsula (certainly high mountains, as Mount Brandon rises to 3,127 feet) and it may be possible to see Kilrush and Kilkee from these.

Actually there is a Dooneen townland by the north coast of the Burren, Co. Clare, but it is on the coast where the coastline is low. With poetic license, one might call the parts of the rocky limestone hills nearby "cliffs", though I very much doubt if one could see Kilkee and Kilrush from them. I often stay at a guesthouse not far away (though just inside Co. Galway) and I asked the son of the guesthouse owner about this; he said he thought it did not refer to an actual place.

Irish OS Map No. 63 does show a Dooneen Point on the Shannon Estuary in Co. Kerry at Grid Reference Q884478 about 4 miles NNE of Ballybunion, and about 2 miles SW of Beal Point. The map shows contours sloping to the north rising up to 30 metres (about 100 feet) in the vicinity. I think it woule be stretching the point to call them cliffs, though they might possibly be rocky (I haven't visited them); they are certainly not on the same league as the Cliffs of Moher in Co. Clare, over 200 metres high. Kilkee is about 7-8 miles north of Dooneen Point, and Kilrush about the same distance to the north-east.

My own opinion as an outsider is that Dooneen Point near Ballybunion is the most likely candidate, but that the song writer used a bit of poetic license to call the area "The high rocky slopes of the CLIFFS of Dooneen". I suppose if they are rocky and sloping, then at least 2 of the 4 words used to describe them ("high, rocky, slopes, and cliffs") are correct.

It is interesting how little we know about the background of songs that presumably are written fairly recently. However songs are meant to be sung and enjoyed rather than analysed.

None of this should be regarded as conclusive. I also have been through Spancilhill in central Co. Clare and it seemed a rather flat and uninteresting place scenically.

The only town called Dooneen (according to an on-line directory http://uk.dir.yahoo.com/Regional/Countries/Ireland/Counties_and_Regions/County_Waterford/Cities_and_Towns/Dooneen/) is in Co. Waterford on the south coast of Ireland.