I think the song you may be looking for is " An Chuilfhionn" pronounced "Coolin or "Fair Haired One". The air is among the oldest and most celebrated of Irish Melodies. From what I remember from the English translation, the first line goes

" I will come to you Coolin/ There at the dawning of another day"

I have been unable to find the Engish and the Irish words which I have somewhere. The recording I have is in Irish and is on the album "CEOL NA NUASAL " produced by Gael Linn back in the late sixties and features among others Sean O' Shea (on vocals, the Chieftains Paddy Moloney on pipes, Sean Potts on whistle, Eamon Butler on Accordion Sean O'Riada on Bodhran, I don't know if it still available, you should be able to contact Gael Linn at Ceornini Gael Linn - 54 Grafton Street. Dublin 2 - Eire.

"An Chuilfionn " is a combination of An Cailin Fionn - Fair Haired Girl