1660 - An Act by the British Parliament forbids the export of Irish wool
1710 - John Forster is unanimously elected Speaker of the House of Commons, replacing Alan Brodrick
1798 - Lord Edward Fitzgerald, a leader of the United Irishmen, is betrayed by Francis Magan; he's arrested and is shot while being apprehended; he dies of his wounds on June 4
1821 - Anna Maria Odell, the second wife of William Odell (former MP for Co. Limerick), gives birth to a stillborn child in the Marshalsea debtors' prison, where she had accompanied her husband
1832 - Standish Hayes O'Grady, scholar, is born in Castleconnell, Co. Limerick
1862 - Máire Ni Aodáin (Mary Hayden), Irish historian, is born
1869 - Birth of Henry Dixon, botanist

I've got till there, is there anything major which happened esp. during the 20th century on this day?

Got these:

19 May 1797: Presses of Belfast Northern Star broken up by members of the Crown Forces drawn from the Monaghan militia.

19 May 1798: Lord Edward Fitzgerald was shot and arrested in Oliver Bond’s house in Dublin. (Dies from wound, 4 June.)

19 May 1798: O'Connell was called to the Irish Bar and became a barrister.

Great stuff, Brandubh.