You will probably get quite a bit of rain and cold, but it rarely rains all day, mostly showers ranging from light to heavy. I only got really wet on the day that I went to Newgrange. It was raining hard at the Hill of Tara and some stayed on the bus, but I ventured out with others who didn't want to miss it ,so my legs got wet. When we got to Newgrange, it was more of a light rain and then cleared up. This was in October, but my first trip to Irelnad was in early May and the weather was about the same, some warmer days, but some pretty chilly too.
I wore a 3/4 rain jacket with hood and on cool days, a wool sweater beneath.
I remember a heavy shower in Galway and that was at the beginning of the trip, light rain in Dingle, light rain at Blarney, and the heavy shower when I was in Dublin at the end.
My advice: have a poncho, rain jacket or umbrella with you every day.
It's a good trip, you'll enjoy it.