Hi Jane,
Thank you for your message.
I have just responded to your query on the Kinawley parish page.
As I mentioned there it may be difficult to find records that go back that far. Catholic records for the parish do not begin until 1820:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Antrim&parish=Carrickfergus&churchid=1142
Church of Ireland records sometimes tend to have earlier start dates so if they family belonged to this church you may be lucky and find some records. Most surviving Church of Ireland records are still held by the local clergy, although some are in the National Archives of Ireland and others are in the Representative Church Body Library in Dublin. Here are their websites: http://www.nationalarchives.ie/ and http://ireland.anglican.org/about/42
It may be an idea to contact the Ulster Historical Foundation for some assistance, however a fee may apply. Here is their email: enquiry@uhf.org.uk
I?m sorry I could not be of more help. 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.
Kind regards,
Genealogy Support
