I am pained to discover no root beer in Ireland.
Have you tried searching in any specialist food shops? There is a place about twenty minutes from here that sells American foods at outrageous prices. If I'm near there I'll often pop in and buy a root beer or grape soda.
Check to see if there are any oriental supermarkets near you. There was a place called Oriental City about half an hour from here, but they were meant to be closing down at the end of May. Last time I was there they were selling cases of A&W for half price. I bought 2, but the girl only rang one through the register so I got mine for 75% off.
I still have 10 cans left. If you buy a ticket on Ryanair from Dublin to Luton, I'm only ten minutes from the airport. If you hurry I might save you a can.