It's great to hear that you are tracing your Irish roots and are interested in visiting Ireland next year.
Before 1864 records were kept in the form of church and parish records so this may be a place to look. The National Library of Ireland
have a website where you can start to look for any records they have. This would be a long process if you do not know which county to start to look in.
There is also the Irish Genealogy website
that has some information on church records and how to search online.
Given that you believe your ancestor John was born in County Cork, this Family History and Genealogy page
may also be of help to you.
Are you hoping to visit County Cork when you visit Ireland next year?