What's the title of the Cartoon Irish Person Theme?

Not “When Irish Eyes Are Smiling,” but the other one; a sort of sprightly jig, played to denote the quality of unambiguous Irishness? It’s used repeatedly in the Warner Brothers short Wearing of the Grin, which features Porky Pig versus some leprechauns, in what must surely be the most authentic and meticulously researched depiction of Irish folklore ever seen in an animated cartoon.

Is it the Irish Washerwoman? http://www.fionasplace.net/Irishmusic/iriswash.mid

I second this, and there’s even a set of traditional parody lyrics: here

Due warning: joke lyrics in very bad taste to follow…

THE TED KENNEDY JIG
O your father is dead
and your mother is dead
and your brother is dead
and your sister’s senile
and your brother is dead
and your brother is dead
and your ex-wife’s a drunk
and your car doesn’t float.

The King of Soup: That sounds like it, thanks!

Dr. Drake: It’s good to know that the hoary tradition of totally insane Scouting songs is apparently still alive and well; I’m sure my web-footed friends will be glad to hear it. But surely “MacTavish” is a Scottish name, not an Irish one? I’d hate to think that the Boy Scouts were confusing their national stereotypes.

Elendil’s Heir: Interestingly, I did a search for the actual lyrics to “The Irish Washerwoman,” and for music that is supposed to represent Irishness, it’s scarcely in better taste than your version. Evidently the song recounts the tale of a bonnie lass who gets married off to a “tough Corporal Casey,” who proceeds to beat the tar out of her on a regular basis until he dies eight years later. And it’s such a cheerful-sounding tune! What the hell?!

I prefer Bullwinkle’s singing waiter version:

Oh, the taters are old and the meat is a fright,
Ev’rything is left over from Saturday night,
We sweep it all up, throw it into a pot,
And we say that it’s real Irish stew that we’ve got!

FYI, the music to Irish songs are reworked and reused over and over again. The lyrics you saw may not be original to the tune.

Many times songs are written to existing tunes many years after the fact. So you’ll get multiple songs with the same base melody.

If you want to get really get confused start trying to collect the names of tunes.