"Birthday of St. Patrick" performed by Leo McCaffrey, appears on the compilation "Ireland's Greatest Hits," RCA CD #66813, 1996. Authorship is credited to "Lover." I guess that would be Samuel Lover, author of When Pat Came over the Hill, Molly Bawn (Or Fair Molly), and The Low-Backed Car.

I was able to transcribe this much from the sound sample at http://www.click2music.co.za/cgi-bin/release.pl?albumid=1532 [What country is ZA? Zambia?]

Now the first faction fight in old Ireland, they say,
It was all on account of St. Patrick's birthday.
Some fought for the eighth; for the ninth more would die,
And who wouldn't see right, sure, they blackened his eye.

Till at last all the factions so positive grew,
They each kept a birthday, so Pat then had two,
Till Father Mulcahy who showed them their sin...

Here's another interesting tidbit from The Voice of a Few Americans - Lincoln's Own Yarns & Stories:

Abe Recites a Song

Lincoln couldn't sing, and he also lacked the faculty of musical adaptation. He had a liking for certain ballads and songs, and while he memorized and recited their lines, someone else did the singing. Lincoln often recited for the delectation of his friends, the following, the authorship of which is unknown:

The first factional fight in old Ireland, they say,
Was all on account of St. Patrick's birthday;
It was somewhere about midnight without any doubt,
And certain it is, it made a great rout.

On the eighth day of March, as some people say,
St. Patrick at midnight he first saw the day;
While others assert 'twas the ninth he was born-
'Twas all a mistake-between midnight and morn.

Some blamed the baby, some blamed the clock;
Some blamed the doctor, some the crowing cock.
With all these close questions sure no one could know,
Whether the babe was too fast or the clock was too slow.

Some fought for the eighth, for the ninth some would die;
He who wouldn't see right would have a black eye.
At length these two factions so positive grew,
They each had a birthday, and Pat he had two.

Till Father Mulcahay who showed them their sins,
He said none could have two birthdays but as twins.
"Now boys, don't be fighting for the eight or the nine;
Don't quarrel so always, now why not combine."

Combine eight with nine. It is the mark;
Let that be the birthday. Amen! said the clerk.
So all got blind drunk, which completed their bliss,
And they've kept up the practice from that day to this.