Here are the only 2 baptism records from www.rootsireland.ie/ for Patrick from both Armagh & Monaghan 1836 + / - 5 years:
Name:Patrick McKennaDate of Birth:
Date of Baptism:19-Sep-1838Address:Not RecordedParish/District:InishkeenGender:MCountyCo. Monaghan
Father:Bernard McKennaMother:Anne McKennaOccupation:
Informant 1:Peter McKenna
Informant 2:Mary Finn
No priest listed.
Name:Patrick McKennaDate of Birth:not listed
Date of Baptism:10-Jun-1835Address:Crehans [creighans], Tehallan Parish, Co. MonaghanParish/District:Tehallan [Tyholland]Gender:MaleCountyCo. Monaghan
Father:Bernard McKennaMother:Anne McElrooOccupation:
Informant 1:James McElroo
Informant 2:Sarah McGourk
Rev. Patrick Carolan, officiated
No McKennas in the 1841 or 51 Irish Census (in any county!)
There are 10 Bernard McKennas & 9 Patricks in Armagh in Griffiths Valuation (free at http://www.askaboutireland.ie/) in 1864; there are over 100 Patricks and 31 Bernards in Monaghan in 1860!
The Tithe Applotments (http://titheapplotmentbooks.nationalarchives.ie/) have 24 McKennas in Armagh in 1827 (no Bernards) & 761 in Monaghan! (16 Bernards)