Robert-
I have made 2 golf trips (1984 and 1994) to Ireland.
As I have gotten older, I have become a big believer in finding one spot that has 4-6 worthwhile golf courses and spending 5-7 days in that area before moving on. I think it is a waste of time and energy to travel about, finding a different place to stay every 2nd or 3rd nite.
I also believe that it is far more enjoyable to play 4 courses twice than play 8 different courses. To me, it is especially enjoyable to play a links course a 2nd or 3rd time, as there are many features (blind shots, slopes, hidden bunkers, etc.) that you might miss on your first trip around the course. Also, the direction of the wind may change and the course may play very differently because of that.
Ireland has a number a regions where you can find enough quality golf to keep you busy for 5 days, while staying at the same hotel/B&B every nite.
Some suggestions -
In and around Dublin: Portmarnock, Royal Dublin, The Island, The European Club, County Louth (aka Baltray)
The Southwest: Tralee, Waterville, Killarney (2), Ballybunion (2), Lahinch, The Dooks (it might make sense staying in 2 places in this area)
The West Coast: County Sligo (aka Rosses Point), Belmullet (aka Carne), Enniscrone, Donegal
The Northwest: Ballyliffin (2), Rosapenna, Portsalon, Narin & Portnoo
The Causeway Coast: Royal Portrush (2), Portstewart, Castlerock, Ballycastle
Those are just the better known courses in these areas. As noted, several clubs do have 36-holes. There are probably a few enjoyable "hidden gems" in each area as well.