Who can initiate an optional referendum at the national level?

Ireland, Constitution (1937, as amended in 2019), accessed 14 September 2022

ARTICLE 27. This Article applies to any Bill, other than a Bill expressed to be a Bill containing a proposal for the amendment of this Constitution, which shall have been deemed, by virtue of Article 23 hereof, to have been passed by both Houses of the Oireachtas. […]

5.1 In every case in which the President decides that a Bill the subject of a petition under this Article contains a proposal of such national importance that the will of the people thereon ought to be ascertained, he shall inform the Taoiseach and the Chairman of each House of the Oireachtas accordingly in writing under his hand and Seal and shall decline to sign and promulgate such Bill as a law unless and until the proposal shall have been approved either

i) by the people at a Referendum in accordance with the provisions of section 2 of Article 47 of this Constitution within a period of eighteen months from the date of the President's decision, or

ii) by a resolution of Dáil Éireann passed within the said period after a dissolution and re-assembly of Dáil Éireann. […]

See also: 

Ireland, Citizen Information, Types of elections and referendums (accessed 14 September 2022):

Ordinary Referendum

An ordinary referendum is one that does not relate to amending Bunreacht na hÉireann (the Irish Constitution). To date no ordinary referendum has ever been held.

An ordinary referendum would take place if the President received a joint petition from both houses of the Oireachtas. The petition would say that a proposed Bill was of such national importance that the people of Ireland should decide whether it became law.

The joint petition must be passed by the majority of the members of the Seanad and one-third of the members of the Dáil. When the President receives the petition, they must consult the Council of State. If the President agrees that the proposal is of such national importance they will refuse to sign the Bill until a referendum has been held.

The referendum must be held within 18 months of the President's decision not to sign the Bill.