Thank you very much for your message. I hope that someone with information on the family makes a connection with you and helps you with your research.
Sometimes doing family history research in Ireland can be very frustrating especially if you do not have a definite parish of origin.
Church records for Kilbrin/Ballyclough parish begin as early as 1807 so if Eugene was born/married there, there will be a record of it:
Perhaps it may be an idea to contact the local parish priest directly to see if he can be of any assistance to you. Here is a link to their contact page:
There are some places where you can search online, however as you pointed out it is difficult to know if the results are relevant without more information.
www.familysearch.org has a huge database of genealogical records including some church records for Ireland.
www.rootsireland.ie have a large collection of Irish Church records, however you have to pay to use this site.
http://churchrecords.irishgenealogy.ie/churchrecords/ have begun a project to upload Irish church records to their site free of charge. So far in Cork only the Catholic Diocese of Cork and Ross have been uploaded. Kilbrin belongs to the Diocese of Cloyne, however it may be worth checking in case they were not born in Kilbrin.
Have you heard of the Tithe Applotment Books? These are earlier land records dating 1823-38. I did a search for Stack?s in Kilbrin and a result came back for Patrick Stack:
Some other websites that you may find useful are:
The National Archives of Ireland http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
The National Library of Ireland http://www.nli.ie/en/family-history-introduction.aspx
Cork Past and Present: www.corkpastandpresent.ie
Genealogy links: http://www.genealogylinks.net/uk/ireland/cork/index.html
Cork Archives: http://www.corkarchives.ie/genealogy/
Irish Newspaper Archives: http://www.irishnewsarchive.com/
The US National Archives: http://www.archives.gov/
Failte Romhat: www.failteromhat.com
Sorry I couldn?t be of more assistance. Hopefully someone will contact you with more information. Please be patient - as our programme has only begun to rollout across the island of Ireland and volunteers in some areas may not yet be organized.