Hi, thank you for your message.
Unfortunately, the reality of finding documentation pertaining to births/baptisms/marriages/deaths in Ireland prior to 1800 ? particularly in rural areas ? is that they simply may not exist.Because the Church of Ireland was the state church in Ireland between 1537 and 1870, record-keeping during this period was difficult for the Catholic Church, meaning few records survive from before the latter half of the 18th century. As the Church of Ireland was the official church of the country the bulk of information that does survive for earlier periods is often from these registers.
For the Church of Ireland Registers check the following sites:
http://ireland.anglican.org/about/42
http://www.nationalarchives.ie
http://www.proni.gov.uk/index/family_history/family_history_key_sources.htm
Most Catholic records are held locally. One website which can be of help is the irishtimes, where it gives an overview of what records are available in specific parishes. For the parish of Lisburn/Blaris follow this link:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Down&parish=Blarisr&churchid=451
And for Belfast City follow this link:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Down&parish=Ballymacarret&churchid=393
You could also check the two land surveys carried out i Ireland during the 19th century for some mention of the family. There are two:
The Tithe Applotment Books (1823-1838) http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
and Griffith's Valuation (1848-1864) found at http://www.askaboutireland.ie/griffith-valuation/
Some other websites which may help you 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
I hope that this helps.
Kind regards,
Genealogy Support