While Full government censuses were taken of the whole island in 1891 these were destroyed by order of the government along with census records for the years 1861 1871 and 1881.
Census records for the years 1821, 1831, 1841 and 1851 were largely destroyed in 1922, in the fire at the Public Record Office Surviving fragments are detailed under the county source-lists.
This means that the earliest surviving comprehensive returns are for 1901 and 1911. Because of this, the normal rule that census returns should not be available to the public for 100 years has been suspended in the Republic of Ireland, and the original returns can be consulted in the National Archives. A full microfilm copy of the 1901 census is available at the LDS Family History Library in Salt Lake City. Indexes, published or database, are available for the 1901 returns of some counties; these are noted under the relevant county. Copies of the 1901 returns for the six counties now in Northern Ireland are available at the Public Record Office of Northern Ireland.
However it is also worth noting fragments of the 1766 census also remain, thanks to the transcribing efforts of Tenison Groves, and the microfilming programme of the Church of Jesus Christ of Latter-day Saints some of these records are available to use. Many other scraps of census material exist in the National Library but are not available to people overseas. The state of the extracts was haphazard and none appeared to be indexed, they are arranged by Parish or Townland. Some number the children or other members of the household. Some only give `widow' or `Mr'. Occasionally an entry only had a surname. The index reads: SURNAME OF HEAD OF HOUSE CHRISTIAN NAME RELIGION -i.e. P = Protestant; C= Catholic D = Dissenter PARISH DIOCESE TOWNLAND COUNTY COMMENTS There is no further detail in the original documents. These can be viewed via the LDS Family History Centre's Microfilm Ordering system. The index was compiled from LDS FILMS 100173, and 100220; the majority of the places covered are in Northern Ireland.
Reakes, J., comp. Ireland 1766 Religious Census [database online] Provo, UT, 2001. Original data: The 1766 Religious Census of Ireland. The Tennison Groves Papers on microfilm LDS Family History Centre, 100173, 1766