Any successful trip with kids begins in the planning phases. Plan activities just for your children, and include them in discussions of sites that you would like to see. You may find that they are just as excited to kiss the Blarney Stone as you are.
Also research playgrounds, public beaches and other places for the kids to get out and run near the attractions you are planning to visit, especially the ones that you know will be hard on the kids. Don't plan too many days of "boring" activities. Try to keep a balance of places you want to go and places they want to go or will enjoy.
If you are short on ideas for good outings with the kids, there are plenty throughout the island. In Dublin you will find The Ark: A Cultural Centre for Children, Dublin's Viking Adventure and the Dublin Zoo, the largest zoo in the country and a favorite of many children. Take them to The Ark to experience one of many cultural performances, or register them for a workshop where they will work side by side with local artists. History comes to life at Dublin's Viking Adventure, where you and your family will interact with "real" vikings in a replica Norse town.
In County Fermanagh, treat the family to a trip to Marble Arch Caves, the first international geopark. The highlight here is a boat ride through one of the world's most famous showcaves.
When in County Kerry stop by Muckross House. Here you will see the famous grand Georgian house, and then take the kids to the nearby reconstructed traditional farming community.
There are also many activities for the kids all over the island involving one of its greatest attributes: beautiful countryside. Take the kids bicycling, horse riding, fishing or on a walking tour. This will give them an activity to keep them busy while allowing you to soak it all in. If you are traveling with older kids, try kayaking, sailing lessons or windsurfing on the coast.
Meals in Ireland can be an experience all their own. Eating out can be terribly expensive in Ireland, but there are ways to get around it while keeping the kids happy. One way to eat on the cheap is to take the kids to the local farmers market.
Another way to curb expenses while making lunch fun for the kids is to take them to a pub. Children of all ages are permitted and welcomed at pubs in Ireland, most of which will have a reasonably priced lunch menu. Irish law requires a person to be 18 years of age to consume alcohol, but older kids especially will love getting to see the inside of a pub.
Picnics are added fun for kids. Many castles and historic sites have picnic grounds, as do all of Ireland's national parks.