Are there any records for population after 1851. to 1861 1871.
The main purpose of the census was to gather statistics (population, occupations, etc.) so once figures were extracted (number of people in a townland, number of children under 10 or whatever) the actual returns were no longer needed which is why many of the early ones were deliberately destroyed.
However, many of the records were completely destroyed prior to 1922, by order of the British government, on grounds of confidentiality.
The original census returns for 1861 and 1871 were destroyed shortly after they were taken.
Documents from the 1881 and 1891 censuses were pulped during the First World War.
The majority of the returns for the four censuses carried out between 1821 and 1851 were destroyed by a major fire at the Public Record Office of Ireland.https://www.bbc.co.uk/news/uk-northern-ireland-27205043My (very. very small) local library has the population figures for the area from each census and I think PRONI in Belfast also has such material for the North of Ireland. Perhaps National Archives in Dublin will have similar for Tipperary and Cork as well as the local archives.
Have you searched to see if 1841 or 1851 were used for Old Age Pension application? Sometimes a sibling of the person you are searching for can be found there.
https://www.familysearch.org/search/collection/2346275What if the family were attached to or working on an Estate how would they have been recorded and did it matter if they were RC or C of I ?
As already stated, everyone would have been included in the original census returns.
I looked in the 1841 for the parents and they are not there and the child is not on the 1851 or the parents.
For Tipperary only fragments of 1821 survive-
http://www.irelandgenweb.com/irltip/records.htm
