Not that I know of. What kind of education are you looking at for your child?
ETA, I do know of at least one private school in Dublin City Centre, but I had also heard some negative feedback. I know there are other private schools around Dublin, but I'm not aware of any in Lucan (I have three kids in school in Lucan).
ETA again! Private primary schools (as in private fee paying, most schools are privately owned) in Ireland in general are rare. If you can say why you are looking for a private primary school, it may be that someone can help you.