The 1901 and 1911 censuses are the only complete surviving census records for the pre-Independence period. Fragments survive for censuses taken from 1821 to 1851 for some counties. These records are available on the National Archives census website can be searched by year, surname, forename and various address fields: www.census.nationalarchives.ie/help/pre1901.html.
The Taoiseach and I recently launched the Beyond 2022: the Virtual Record Treasury of Ireland, an all-island and international collaborative research project to create a virtual reconstruction of the Public Record Office of Ireland, which was destroyed in the opening engagement of the Civil War exactly one hundred years ago. This includes returns for the 1766 religious census of Ireland, are one of the richest sources available to the historical and genealogical researcher for the period prior to the commencement of the statutory census series. Over 50,000 names of individuals across all religious denominations have been transcribed from these sources. See: virtualtreasury.ie/gold-seams/1766-religious-census.