We are traveling to Ireland in March and looking for things to do in Galway and Dublin with a 4 year old. We are looking for the best things to do specifically for him, not for the grown ups (already have that worked out). We'll also be in Dingle if you have ideas for little kid friendly activities around there!
Galway has lots of street musicians and other street performers such as jugglers. Your child might enjoy watching them. You can easily move on whenever he gets bored. Salthill (walk or bus from Galway center) has some sandy beach areas that you son might enjoy planing in if it is not too cold and windy in March. I know that the Atlantiquaria is a well known aquarium in Salthill though I did not visit it.
The Dead Zoo? Better known as the Natural History Museum. There is also an actual zoo out in Phoenix Park.