Wow, interesting question. Nature-wise there's SO much to see in Ireland - Cliffs of Moher, Giant's Causeway, the Dingle Peninsula. There's sights from Blarney Castle to the amazing history and sights of Belfast.
However, if you're after things specifically that children may enjoy - 'history' stuff is probably out ;) I'd suggest the following to include in your itinerary:
1) Dingle Peninsula - as well as being a beautiful place and a charming town, you can look for Fungie, Dingle's resident dolphin. And if you can't find him, his statue is down by the boats as well :)
2) Giant's Causeway - a spectacular place with over 40,000 columns of basalt rock, it'd be fun for kids to climb all over as well.
3) The Exploris Aquarium in Northern Ireland: http://www.northern-ireland-travel.com/exploris-aquarium.html
4) Belfast - the night-time Black Cab tours - sure the history won't mean much to the kids, but Black Cabs can be a fun and different vehicle to ride in. And it's a brilliant tour for adults!
5) Blarney Castle - castles are fun for everyone, and you get to hang off the top and kiss the Blarney stone! ;)
6) The Cliffs of Moher can't be skipped - absolutely spectacular! Plus when you see the Cliffs of Insanity in The Princess Bride, you'll be able to say you've been there :)
Finally if you're after some places to eat and stay that are kids friendly: