DCarey,
Statutory registration only started in Ireland in 1864 so you won’t find birth or marriage certificates for this family. Normally we rely on church records before 1864 but in the case of Aghadowey (RC parish of Killowen) their records don’t start till 1843. This was the only McCloskey family in Aghadowey parish in the 1831 census. Headed by William, they lived in Cloggan & Resk and the family comprised 4 males and 5 females, plus 1 servant.
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Coleraine/…
William is listed in the 1831 tithes for Cleggan and was therefore a farmer: http://www.irishgenealogyhub.com/derry/tithe-applotments/aghadowey-pari… A John McCluskey was still farming there in Griffiths Valuation c 1860 (plot 1, a 23 acre farm). He was succeeded by Thomas in 1862 and then by a John (not necessarily the same John) in 1865. He had gone by the time of the 1901 census. John’s name is deleted from the Valuation Records in 1897. (The property today is on Clagan Park off the Agivey Rd).
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee. The North of Ireland Family History Society is running an Ulster DNA project in conjunction with FTDNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).