We have not been yet but I just saw on the museum's website that Children and families are welcome and all children under 3 go free. Children over 3 pay the student concession rate of €4. Keep an eye out on its Twitter and Facebook pages for other free-in times for kids, which it runs throughout the year.
There is a special online family admission rate of €8 at the moment (usually €13) and it covers 2 adults and up to three children.
If you are visiting with children, it has worksheets available at the museum for children of all ages and the website says the museum has tour guides in the museum at all times who can give children some special attention. There are some interactive artefacts in the museum which kids can handle - just ask a tour guide to point them out to you. You can also take a picture of your child in the old Dublin school desk, or make a speech from JFK’s lectern.