Constantinople is sieged again shortly after hour POD, and falls to the Muslims. Then, Islam gradually spreads, in fits and starts, across Europe, aided by the eastern peoples converting.
This, really. In order to make Ireland dominated by Islam, you must first make all of Europe dominated by Islam. Ireland is probably the last country to become Muslim due to its geographical position. However, if Constantinople falls shortly after the POD, I assume Russia would voluntarily choose Islam, like they accepted Orthodox Christianity in OTL. After this it would have to spread relatively fast westwards. You would probably have to use conquest in the areas that were already Christian. I think it would take a lot of wanking in order to make Ireland majority Muslim.