You can definitely obtain a copy of the 1911 and 1901 census from the National Archives in Bishop Street. You need to go in there though. If it's Dublin, you can also get them from the library on Pearse St. Both sets are on microfiche. The staff are helpful.
The 100 census rule was relaxed in the 1960s for these 2 censuses because of the lack of earlier 19th century information. The 1891 and 1881 census returns were pulped for paper during WW1. The British army mistakingly believed there to be a second copy of each return. Earlier returns for 1861 onwards were lost when an incendiary device hit the 4 courts during the civil war.
The next release is in 2025 of the 1925 census.
Hope this helps.