January–February - The 'Great Frost' continues: unusually harsh winter followed by a Spring drought.
April - Citizens of Drogheda prevent food being exported from their town to Scotland.
May 31–June 2 - Bread riots in Dublin.
June–December - Exceptionally cold weather, leading to the Great Irish Famine (1740-1741).
First steam engine installed in Ireland, for pumping at Doonane Colliery, Shrule.
A Dublin–Belfast stage coach service runs.
Conolly's Folly in the grounds of Castletown House, County Kildare, commissioned by Katherine Conolly from architect Richard Cassels, is erected to provide employment for hundreds of the poor of Celbridge during the Famine.
The original Ballymena Castle burns down.
April 7 - Armar Lowry-Corry, 1st Earl Belmore, politician and High Sheriff (d. 1802)
October 22 - Philip Francis, politician and pamphleteer (d. 1818)
Richard Barrett, poet and United Irishman (d. 1818)
John Foster, 1st Baron Oriel, politician and Irish Chancellor of the Exchequer (d. 1828)
Edmund Garvey, painter (d. 1813)
Nathaniel Grogan, painter (d. 1807)
James Napper Tandy, rebel leader (d. 1803)
May 13 - Thomas Milles, Church of Ireland Bishop of Waterford and Lismore since 1708 (b. 1671 in England)
c. June - Bernard O'Gara, Roman Catholic Archbishop of Tuam
December 1 - John Abernethy, Presbyterian minister (b. 1680)
1740 in Ireland Wikipedia
Events from the year 1740 in Ireland.