WILLIAM MCKENNA

Griffiths Valuation has 7 listings for Owen McKenna in Armagh in 1864:

http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch

They are in 5 civil parishes.  Assuming your Owen was still alive in 1864 then one of them might be your family. You don’t say what denomination the family was but I suspect RC. You can search the RC parish records on this link:

http://www.nli.ie

Not all RC parishes have records for 1827, so there may be gaps. I see a baptism for a William McKenna to Owen McKenna and Mary Hughes on 11th July 1824 in the parish of Tynan. I have no way of telling whether it might be your William though. William McKenna is a fairly common name in Armagh.