The 1892 marriage in Ulster Historical Foundation ancestryireland.com ., is for an Anne Rogan, it has a possible match year with a Henry Carlin in both cases the fathers name is not mentioned.
As an alternative I went to GRONI
https://www.nidirect.gov.uk/articles/search-gronis-online-records#toc-0 for a free look up follow on the instructions, you will arrive at Purchasing Credits Page on the right hand side is a box marked
Free search then entering Carlin Henry enter Year from 1891 to 1892 and then do it again for 1892 to 1893 the result for both is one marriage recorded. proving the marriage is 1892 Do the same for Ann or Anne Rogan and the results are zero. So assuming its under Rogan but perhaps with a first name of two first names etc the answer is 4 marriages 10 for 1892 to 1893.
So you could search just for Henry Carlin marriage 1892, all you need for the Henry Carlin 1892 is a credit costs £0.50. You can hold up to a maximum of 200 credits.
You need a minimum of one credit in your account before you can search the records.
ie 50p on a credit or debit card cost of one search. buying a certificate of what your result is a further charge if you need one is £15.
When you think no other way forward, then for 50p I think its your back stop even if it turns out to be the wrong marriage
