We fly into Dublin and arrive on March 13th and fly out of Dublin on the 19th. We are renting a car and need help deciding what are the road trip must see that are realistic in our time frame. Definitely would like to visit the Blarney Stone and Cliffs of Moher. Any suggestions on an itinerary would be much appreciated.
March 13th suggest Dublin via Cashel (rock of Cashel) to Blarney and on to Killarney
March 14th In Killarney See Muckross house and gap of Dunloe and lakes 
March 15th Dingle and west and Fungi  (overnight Dingle)
March 16th Dingle  via Tarbert  ferry to County Clare and Cliffs of Moher and on to Galway
March 17th in Galway  St Patricks Day  Parade and fun and pubs
March 18th Galway to Dublin 
This itinerary looks great. Are you saying to drive out of Dublin to Killarney the first day and staying the night in Killarney or staying the night in Dublin and drive on to Killarney on th 14th?
its about 4 hours driving from dublin airport to cashel to  blarney to killarney
dublin to cork is all motorway so easy and fast 
allow 3 hours for stops total about 7 hours
depends what time you get into dublin
If you spend first night in dublin then skip dingle so that you are in galway for st patrics day