I'd love to see what I can do to help you find out more! 😊
Where have you been looking so far? On the Catholic Parish Registers page I was able to find Allihies Parish
in the Diocese of Kerry in County Cork. On that page, you can also browse through the microfilms that are available.
Another helpful tool is the Irish Genealogy page, where you can search through the available Church records
, as well as the Civil records (all the records after 1864). There are quite a lot of search results for John Sullivan around that time. Do you happen to know the names of his parents or perhaps his siblings?
You mentioned your Great Great Grandparents getting married in Allihies Parish. Do you know what year they got married, and the name of your Great Great Grandmother? This will make it easier for you to search through the records.
I hope this was helpful, and hopefully, some of our expert members will be able to help out as well.