The problem with this is you're asking for an accent, but accents are super super different all over Ireland. The Belfast/Northern Irish accent sounds nothing like a Dublin accent or a Cork accent. While Irish is taught in all schools in the Republic and some schools in the North, it isn't generally spoken in public by the vast majority of people. That is more likely to happen in Gaeltach (Irish speaking) areas. The Gaeltach areas (mostly rural western and southwestern Ireland where Irish is spoken on a regular basis) have even more different accent.
I'd start here :
http://www.bbc.co.uk/northernireland/irish/blas/
The page itself is in Irish, but there are links to the right with "beginner blas" that have tutorials with audio on how to pronounce general things.
And there's also a link to Radio Ulster's regular Irish language radio programming.
Also, to listen to other accents/get county news, try
http://www.rte.ie/ RTE is the BBC equivalent for the Republic of Ireland.
ETA: sorry for the N. Ireland emphasis
