If you're looking for Irish records prior to independence, then you may struggle.
A large proportion of the then-surviving parish records were destroyed during the civil war in 1922 - including the majority of the early census returns: the only surviving complete census sets prior to this period are 1901 and 1911. Some parish records survived, but coverage is patchy at best.
Ruth
Many Church of Ireland records, originally sent to Dublin for safe-keeping, were destroyed in Dublin. Survival of other denomination's records vary greatly.
The 1831 census for County Londonderry does survive but only lists head of household giving number of males a & females and number by denomination.
