Seven comments
Not A Polka
But a fantastic slow air, not to be played with strict metre, but freely. (Not sure of the musical term Rubarto?)
Riverdance
I think this was composed by Bill Whelan for Riverdance. Or am I mistaken?
Rubato, by the way, is the standard musical term for slight variations in tempo. This tune could be approached as "molto (very) rubato" or even "ad libitum" (i.e., "ad lib," meaning freely).
Pronunciation
In case anyone is wondering, the pronunciation is something like “kwinnuh koo ĥullin”—not scientifically exact, but a reasonably recognizable anglicization.
The transcription isn’t quite right, I think, but it works if you listen to it as well. There’s a great performance available online at http://www.youtube.com/watch?v=WSjmvU_8xLY.
Cú Chulainn is a mythological Irish hero—sort of the Celtic equivalent to Achilles.
Davey Spillane ABCs??
Does anyone have the notes (letter notation preferred but beggars can’t be choosers) for this air as played by Spillane?
Here is the currently working link to his version if you need to hear it
http://www.youtube.com/watch?v=vDyMFP6yzfk
Term
"Not sure of the musical term Rubarto?"
The musical term is Rubato. You were close, but not quite.
Here is a really nice version of the Lament, Caoineadh Cu Chulainn, on the Low Whistle by Olaf Vize
Wexfords First Rebellion 1793
According to sleeve notes of recording called Fonn, by local Enniscorthy musicians - this was composed by Davy Spillane and recorded in Sept 2000 for a video production "Wexfords First Rebellion 1793" by Carraigbyrne Film Productions Ltd. Thanks are given to Bill Murray for permission to use. https://thesession.org/recordings/4391
The 1798 rebellion is very well known in Ireland but must admit, I had not heard of a Wexford Rebellion in 1793. However apparently it did indeed occur and is not a typo!