Thank you for your message.
As you have census records I assume that you have Luke?s date of birth. With this you could try and find his baptismal record in the parish records, most of which are held locally. You could try writing to the parish priest for possible assistance. One website which you may find useful, however, is the Irish Times where they give an overview of what records are available in specific parishes. For Fermoy parish follow this link:
You could also search for him at https://familysearch.org/ This is a huge online database of genealogical records that has been compiled by the Church of the Latter Day Saints.
Another online database of Church records is Roots Ireland, however please note that you have to pay to use this site. Here is the link:
Do you know Luke or Catherine?s parents? names? If you do, you could searching for them in the Tithe Applotment Books. These are land records compiled between 1823 and 1837 in order to determine the amount which occupiers of agricultural holdings should pay in tithes to the Church of Ireland. Although they do not give any genealogical information they can be used to tie a person to a specific place. You may even find Luke in them. You can search them here:
You should probably also try the later record called Griffith?s Valuation (1848-1864):
Have you looked into the family?s emigration much? Sometimes more information was given at the port of arrival rather than that of departure so you may find confirmation of place of origin here. For information on US immigration records go to the following link:
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
The Public Records Office of Northern Ireland http://www.proni.gov.uk/index/family_history.htm
Failte Romhat: www.failteromhat.com
Genealogy Links: http://www.genealogylinks.net/uk/ireland/cork/index.html
Census Records 1901/1911: http://www.census.nationalarchives.ie/search/
Alternatively you could try contacting Mallow Heritage Centre in North Cork for assistance- a fee may apply. Here are their contact details:
Mallow Heritage Centre,
27-28 Bank Place,
Phone: +353(0) 22 5032 Email: firstname.lastname@example.org
I hope that this is helpful. Best of luck with your research!