The Curragh Golf Club was founded in 1883 but apparently the golf course dates from 1852, making it the oldest in Ireland.
I think the Curragh, Portsalon and two or three other courses were the founding members of the GUI.
Here's something I found on the In-ter-net.
"In 1851 David Ritchie came to Ireland from his native Edinburgh, where he had been a member of the ancient golf club at Musselburgh (founded 1774). On his death in 1910 it was reported that he claimed 'to be the oldest golfer in Ireland, as he had ample proof of playing with the late Mr. Alexander Love on links he organised on the Curragh in the early 1850's. In 1852 the Earl of Eglington, who was British Lord Lieutenant of Ireland and founder Captain of Prestwick Golf Club (1851), played on the Curragh. On 12th March 1883 the Irish Times newspaper carried the following announcement: 'Maj. Gen. Fraser, V.C., C.B Commanding the Curragh Brigade, has sanctioned the formation of a garrison golf club. The Rules of the Club will be the same as those of the Royal and Ancient Golf Club, St.Andrews.' Membership was confined to Officers of the Curragh British Garrison and there was neither an entry fee or subscription. By 1889 the course was eighteen holes and affiliated to the Golfing Union of Ireland. On 24th September 1910 the title 'Royal' was conferred on the Curragh Golf Club, a title, though not normally used, is still valid.
The Curragh Golf Club continues to maintain a tradition of military and civilian participation in the management of it's affairs. The Club centenary in 1983 was marked by the presence of the Captains of the Royal & Ancient, Royal Musselburgh and Prestwick, all of which have historic connections with the Curragh. "