Hi,
Thank you for your message.
Have you tried looking for John and Lucinda in church records?
Most Catholic records are held locally. One website which may help you is the Irishtimes website. Here, they give an overview of what records are available in specific parishes. For Tartaraghan/Loughgall Catholic parish follow this link:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Armagh&parish=Loughgall&churchid=227
For Tandragee/Ballymore Roman Catholic parish follow this link:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Armagh&parish=Ballymore&churchid=192
For Church of Ireland records check: http://ireland.anglican.org/about/42 and http://www.nationalarchives.ie/. The Anglican Record Project is has created an index to their records: http://ireland.anglican.org/cmsfiles/pdf/AboutUs/library/AngRecord/bunclodyunionindex.pdf
Also check http://www.proni.gov.uk/index/family_history/family_history_key_sources.htm
You could also do a search in the land records pertaining to Ireland in the 19th century. There are two:
The Tithe Applotment Books (1823-1838) found at http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
and Griffith's Valuation at http://www.askaboutireland.ie/griffith-valuation/
If you can find any family that remained in Ireland, you could check for them or their descendants in the 1901 and 1911 census records at http://www.census.nationalarchives.ie/search/
Some other websites which may help you in your search 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 National Archives UK ? genealogy search: http://www.nationalarchives.gov.uk/records/looking-for-person/
The Public Records Office of Northern Ireland http://www.proni.gov.uk/index/family_history.htm
Family Search: https://familysearch.org/
I hope that this helps. Remember to post any new information you come across as the more information you post the more likely is is that one of our volunteers will be able to help you.
Kind regards,
Genealogy Support