The tune of which you speak is likely "An Coolin." "An" is the Irish word for "the."

I've heard many versions of the title, but the one I like best suggests that "the coolin" was like a pig-tail or pony worn by Irish Farm labourers back a couple of centuries ago. When they were leaving for whatever reason, emigration, banishment, transportation, they would cut off the hank of hair and give it to their mother or their sweetheart to remember them by.

I've also heard it said that a "coolin" is a little bird, but I like the first version better.

Maybe someone with a knowledge of Irish could elaborate

Jack Hickman