The Irish presidency is the weakest of all countries with a semi-presidential constitution. However, occasionally, the president does use what few powers are invested in the office.
Art. 26. 1. 1 of the 1937 Constitution states: “The President may, after consultation with the Council of State, refer any Bill to … the Supreme Court for a decision on the question as to whether such Bill or any specified provision or provisions of such Bill is or are repugnant to this Constitution or to any provision thereof.”
So, the president does not have the power to veto legislation or to ask the parliament to consider a bill for a second time. However, once a bill has been passed and before it is promulgated, the president may, after convening an advisory body, refer the bill to the Supreme Court, which then determines its constitutionality.
This power has been used relatively frequently. Wikipedia has a very informative table listing all the occasions when this Article has been invoked and identifying the outcome.
Basically, three scenarios are possible: the president signs the bill; the president refers the bill to the Supreme Court, which approves it; the president refers the bill to the Supreme Court, which strikes down all or part of the bill. All of these outcomes have occurred at some point.
Anyway, on 21 December President Mary McAleese convened the Council of State to take advice about the Credit Institutions (Stabilisation) Bill 2010 – otherwise known as the huge IMF and EU bailout of the bankrupt Irish banks bill! The president decided not to refer the bill to the Supreme Court, so it has become law and its constitutionality cannot be challenged.
Obviously, Ireland has a weak president. As I said, it has the weakest president of all countries with a semi-presidential constitution. All the same, the president does have a few powers. These powers are occasionally used and when they are used they can be controversial.