It's common at this time of year for adults to ask small children What's Santy bringing you? (awkward as this is for those of us who don't celebrate Christmas). Is this pronunciation of Santa unique to Ireland?
I've heard it once in my life here in the U.S. We certainly have no shortage of such diminutives - dearie, doggy, Marty, Lindy - but that's one that seems to have dipped its toe in the Atlantic and decided the water was too cold to cross over.
A notable outlier is Tim Burton's The Nightmare Before Christmas, in which the characters refer to the St. Nick character as "Sandy Claws".
There was a 1933 American cartoon short named "The Shanty Where Santy Claus Lives".
The first words spoken (by the small boy protagonist; in an American accent) are "Santy Claus!"
So, no, the pronunciation is not unique to Ireland, although from other people's answers, it seems to be rare in modern times.
There is an instance of 'Santy' in the (at least formerly) popular children's Christmas special Winnie the Pooh and Christmas Too. Tigger says 'Santy', though I'm not sure if he's supposed to represent a demographic that speaks as he does. Having been raised on Winnie the Pooh, it would not surprise me if a person said 'Santy'.
the Marx Brothers, through Chico's Italian-American-esque dialog in A Night at the Opera (USA, 1935), hints of either "Santy" or "Santa" clause. I always thought he was referencing the "Santy" version. the interpolation of "i" is the dialect-mangling, but the "y" suffix has no origin in the dialect (that I'm aware of).
Groucho: "That's in every contract, that's what you call a sanity clause."
Chico: "You can't a fool a me there ain't no sanity clause"
Additionally, the classic (ahem) film Santa Claus Conquers the Martians (USA, 1964) has an 'a' in the title and and an 'a' in the spelled lyric, but the song Hooray for Santy Claus is pronounced and transcribed as Santy.
Hooray for Santy Claus!
You spell it S-A-N-T-A, C-L-A-U-S
Hooray for Santy Claus
If you've never seen a 1985 film called "Lost in America," I highly recommend it. The movie's hilarious.
Why am I mentioning a 30-year-old film? Because there's a very funny, memorable scene involving Garry Marshall and the phrase "Santy Claus." The scene takes place in Las Vegas, quite a distance from Ireland!