from my Irish Genealogy A Record Finder the following::
The British Library has an impressive accumulation of Irish Newspaper material at Colindale, and the National Library (Dublin) possesses a copy of their catalogue to this material. Before 1826, the papers are somewhat fragmentary but from then on the British Library was required to hold all the Irish papers, so moderately complete runs may be expected as from that date.
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So try looking here: (the book I quote was written in 1987)
://www.bl.uk/reshelp/inrrooms/blnewspapers/newscat/newscat.html