The census for both years can be seen in the National Archives , Bishop St., Dublin 8. The Old Age pension was introduced in 1908. Often to prove a birth before official registration in 1864 a search was made of 1821-1851 census. Some of these records survive in the National Archives. As almost all census records for the 1800's were destroyed the only alternative is to use 'Census Substitutes'.
Theses are usually land related records.
The Griffith's Valuation of Tenements which was done from 1848-1864 covered the whole country. A computerised list sorted by surname on computer can also be searched in the genealogy room in the National Library. If my ancestors lived on farm in Ireland after 1850's are their any other related records. If you found record in Griffith's Valuation for your ancestor's farm then you can also see records in Valuation Office. They hold 'Cancellation Books' which were subsequent valuations which also show when farm changed ownership.