You say that you think the family may come from Clady Beg. That townland is in the RC parish of Ballymacnab (civil parish of Kilclooney) not in Killevy. Ballymacnab’s marriage records only start in 1844. Baptisms start in 1820. Those records are on the rootsireland site (subscription).
My reading of the Clady Beg records in Griffiths 1864 is that John Cosgrove held 11 acres of land on plot 16. There was also a house there but he didn’t live in it and instead sublet it to John McGuinness and another. So John was living somewhere else nearby. Since he isn’t otherwise listed in Griffiths for that parish I’d guess he stayed with one of his relatives, and so doesn’t show up.(Only heads of household are listed in Griffiths). By 1869 Bernard has taken the land over suggesting John may have died. There is 1 death in the stat records that fits. That’s for John Cosgrove died 23.3.1871 aged 60. Registered in Armagh city. You can view the certificate on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
(You will need to open an account and buy some credits. It costs £2 to a view a certificate).
Returning to the land valuation records, plot 16 changed to Patrick in 1880 at which point he was also occupying the house on the land. In 1893, it changed to Catherine (his widow perhaps?) and finally in 1896 the farm reverted to the Charlemont estate.
A Patrick Cosgrove died on 23.6.1888 at Clady Beg, aged 95 (see probate abstract below). He seems too old to be descended from John. (Could be a brother perhaps). There’s another Patrick Cosgrove death registered in Armagh 25.2.1892 aged 53. Perhaps that’s the former tenant of plot 16?
PRONI has some probate abstracts for Cosgroves of Clady Beg. Some of the wills are on-line. Some are not and you would either need to go to PRONI in person or pay them to copy them, if you want to read them.
The Will of Henry Cosgrove late of Cladybeg County Armagh Farmer deceased who died 9 April 1881 at same place was proved at Armagh by John Gollogly of Cladybeg and George Taylor of Cladymore both in County Armagh Farmers the Executors.
Letters of Administration (with the Will annexed) of the personal estate of Patrick Cosgrove late of Cladybeg County Armagh Farmer who died 28 June 1888 at same place were granted at Armagh to John Cosgrove of Cladybeg a son and a Legatee.
(The above will is on-line on the PRONI wills site. Patrick was evidently a widower. He left the farm to his son John. Other sons were Felix, Francis, James & Patrick).
Administration of the Estate of James Cosgrove late of Cladybeg County Armagh Farmer (Retired) who died 31 January 1910 granted at Armagh to Sarah Cosgrove Spinster
Cosgrove Patrick of Cladybeg county Armagh farmer died 10 December 1923 at Ballymacnab county Armagh Probate Belfast 5 June to Michael Clarke and John Vallely farmers. Effects £2.
Cosgrove Peter of Cladybeg Mowhan county Armagh old age pensioner and farmer died 21 June 1951 Probate Belfast 26 September to Sarah Golloghy spinster. Effects £69.
There were other probate files for Cosgroves in the adjacent townland of Clady More.
http://www.proni.gov.uk/index/search_the_archives/will_calendars.htm