Frances,
I looked for a death certificate for Hannah 1864 to 1874 but did not find any of that name in the Kilclooney registration area. Likewise I could not find a death for James in 1867 born c 1794.
There are some trees on Ancestry that have this family but all had these events in Glenties, Co Donegal. That’s 100 miles from Co. Armagh. There are a couple of townlands (not parishes) in Donegal called Kilclooney. I wonder if there has been some confusion in identifying the correct county here?
You have put this query under Co Armagh. However Kilclooney is in Co Donegal. You might want to re-post your query under Glenties, Co Donegal to get a better response.
I assume the family was RC. If so the bad news is that Glenties parish has no records before 1866, so you will probably struggle to find much about the family.
Have you obtained copies of James & Hannah’s death certificates? You may get a little from that. I see a John & James Martin in Kilclooney Beg in Griffiths Valuation c 1860. They were farming plot 4 together with James Kennedy. That was a 17 acre farm. John & James were probably closely related, brothers perhaps?
There were still some Kennedys there in the 1901 census but no Martins.
http://www.census.nationalarchives.ie/pages/1901/Donegal/Dowras/Kilcloo…