Do I need rain boots for Ireland in April/May?

If you are talking about Wellington boots then no. But I would suggest a waterproof shoe if you plan on walking around the west coast of Ireland. I wore a pair of North Face Gortex shoes (hedgehog). They kept my feet perfectly dry. In fact, I was the only one in the group of 14 on the tour that had dry feet. It will rain and you will still need to be outdoors - so prepare. make sure you have a good waterproof jacket.

I recommend waterproof hiking shoes. Boots are not necessary. I wore my Keens on the Cliffs of Moher and it rained the whole time over a half hour hike. I had my umbrella and raincoat too. The shoes were the least of my worries when it came to getting wet, as the raincoat is on the old side and the wind blew the misty rain under my umbrella.

I agree that unless you plan to do some serious hiking, waterproof boots would be overkill. For casual walking a good pair of waterproof shoes would be enough.
A quality Goretex outer shell would be a good idea too.

OK then I think I will look for some waterproof walking shoes (I saw some Clark's Wave ones that looked comfy) and also bring a good waterproof rain jacket & umbrella. Thank you for your suggestions. As always, much appreciated.

Diana, consider two things. Try to find a good rain coat (long length) rather than a jacket (short length). Makes all the difference in the world. Also, no matter how good the shoes, take an extra pair of socks in your day bag just in case. Having them has saved the day on several occasions.

TC - I have a nice London Fog trench coat style rain jacket that I'm planning on taking with me. I also bought those Clarks Wave sneakers which are supposed to be waterproof. Thanks for the tip on extra socks in my day bag. I'm sure that will be useful.

We all got waterproof shoes and waterproof jackets. However all of our jackets are regular length ones. I'm wondering if we're going to need rain pants too?

We are going in late may

make sure your boots/shoes/sneakers are broken in before your vacation