March - Jonathan Swift publishes the first of the Drapier's Letters (A Letter To the Shop-Keepers, Tradesmen, Farmers, and Common-People of Ireland, Concerning the Brass Half-Pence Coined by Mr. Woods).
March 24 - Richard Hamilton, 4th Viscount Boyne, politician (d. 1789)
October 20 - Thomas Taylour, 1st Earl of Bective, politician (d. 1795)
John Hely, later Hely-Hutchinson, lawyer and statesman (d. 1794)
John Pomeroy, British Army officer (d. 1790)
Frances Sheridan, novelist and playwright (d. 1766)
1724 or 1725 - Arthur Guinness, brewer (d. 1803)
Robert Blakeney, politician (d. 1762)
Frances Greville née Macartney, poet (d. 1789)
February 10 or 1723 - Henry Colley, politician (b. c.1685)
November - Liam an Dúna Mac Cairteáin, poet and soldier (b. 1668)
John Barnwell, colonist in the Province of South Carolina (b. 1671)
Approximate date - Proinsias Ó Doibhlin, poet and priest.
1724 in Ireland Wikipedia
Events from the year 1724 in Ireland.