Your best bet to find a wife's maiden name is a birth record from one of their children. In Ireland birth records have
mother and father's names and mother's maiden name.
The issue might be records for Edward Cochran's children and if they go back far enough.
Two options are www.emeraldancestors.com
free to look & fees for a record.
an Irish History Foundation with bmd's for Armagh.
It is a not for profit but pay website. There are only two Parish's in Armagh that reach back to the late 1700's. The next start 1814 and higher.
You might be able to find inscriptions for gravestone's for Armagh, try libraries, Heritage & Museum societies for journals. In 1900 Ireland underwent sort of a census of readable gravestones.
There is a website for History from Gravestones, I don't have the exact name but you should be able to google that.