7 January – Dáil Éireann debated a motion that Éamon de Valera's position as controlling director of the Irish Press newspaper could be regarded as incompatible with his duties as Taoiseach.
23 January – The government was considering the introduction of a pay-as-you-earn system of income tax.
22 September – At its inaugural conference the Irish Congress of Trade Unions attacked the government of Northern Ireland for not recognising the new organisation.
4 October – Three men collapsed and died at Croke Park during the All-Ireland Hurling Final Replay.
4 December – Twelve new female members of the Garda Síochána (police), known as ban gardaí, passed out of the training depot in the Phoenix Park in Dublin.
Figures released on 4 February 1960 showed that 118 million telephone calls were made in 1959.
12 February – The first edition of the Irish Music Charts Top 10 was printed in the Evening Herald newspaper. Elvis Presley's "One Night" became the first song to top the charts. (The official charts were founded by RTÉ in 1962.)