If John Cunningham re-married after 1845 in a non-Catholic ceremony he should be in the civil registration index.
Mulnagore is in Pomeroy civil parish and Dungannon Poor Law Union/civil registration district.
Possible marriage?
20 Dec.1859 Killeeshal Co.Tyrone: John Cunningham, widowed, son of William Cunningham to Isabella Hoey, single, daughter of William Hoey.
Killeeshil is the name of a townland and civil parish in Dungannon PLU/registration district. It's less than 10 miles from Mulnagore.