The Dunbrody is a great experience for tourists, and you can stay around & poke into all the little nooks and crannies.
The Jeanie Johnson is often in Dublin, and can be rented out for corporate events. It's also available like the Dunbrody as a once-off visit.
http://www.jeaniejohnston.ie/ The Dyflin is a not terribly authentic replica of a viking ship, decaying around the Dublin docklands somewhere. I haven't seen it in about five years ago - since then, someone set fire to it while it was moored up in the middle of the Liffey.
There is a small viking skiff in the INHP in Ferrycarraig, Wexford. But it's locked away from prying eyes in a decaying viking shipyard for some reason.
If you like boats, I'd recommend getting to the Ship Museum in Roskilde. It's where the magnificent Havhingsten was built. They have over 20 ships, some 200 year old originals, some replicas of local finds. It's great.
John