Irish records can be challenging as many were lost over the years for different reasons and those that are available are spread over many sites, both free and paid.
Often you need to think totally outside the box to search, but always need the actual records to confirm your findings as many names are the same and you can follow the wrong line quite easily.
based on a search of
www.rootsireland.ie a paid site
using Michael NEARY and Catherine HANLON as parents
combined with a search on
www.familysearch.orggave the following results
Margaret NARY b./bap. 1860
Sarah NEARY b./bap. 1862
Catherine NEARY b. 21 Aug 1864
Michael NEARY b./bap. 23. Oct 1866
Bridget NEARY b./bap. 1869
Eliza NEARY b./bap. 27 Mar 1871
Patrick NEARY b./bap. 14 May 1873 (rootsireland shows 1859 also)
Patrick's marriage, interestingly, looks like
Kilkenny Oct-Dec 1895 V3 P345 to Kate FLOOD
Hope that this helps - if the cert from the GRO confirms the names at least you're on the right track! If I located a correct prison record for James FitzPATRCIK in the 1890s at the time he lived on the same street in Kilkenny as my OH's ancestors!