Statistically, October and November are the wettest months across most of Ireland.
However, Ireland's maritime climate means rain falls every month. No true "dry season" exists. Summer (June–August) can be wet; winter (Dec–Feb) brings steady drizzle. The west coast (Galway, Kerry) receives 2× the rainfall of the east (Dublin).
Practical tip: Pack a waterproof shell year-round. "Four seasons in one day" is a reliable forecast.