I know the Kennedys were Presbyterian "Northies," self-identified as such in family lore.
There is a marriage certificate for John Kennedy and Margaret/Pegey Jane Bamford at First Garvagh on 4 Mar 1839 via RootsIreland.ie. There was a Bamford family in Lisheegan townland in Finvoy. Culnamen seems to be less than 10 miles from Lisheegan, even less as the crow flies, though there is a river between the townlands.
If you go here
http://www.oocities.org/heartland/ranch/5632/bv/moneydig_mgrs.html you will also find information on visitation to the Kennedy family in Culnamen (Cooleymen, as it's spelled there), listing a family of Kennedys including a Samuel, John and Hugh. My GGGG-GM Margaret Bamford Kennedy was buried in a plot belonging to Hugh B. Kennedy, who I am assuming is her son.
John and Margaret/Pegey had children named John, Samuel, Hugh, Thomas and Elizabeth (leading me to believe Margaret/Pegey's parents were Thomas and Elizabeth).
Perhaps the Kennedys moved from the First Garvagh church to the Moneydig church, which was built later (1830s?). I can't seem to find full records for Moneydig.
Edited to add: the records in Ireland tend to say Bamford; on Margaret's record for the cemetery she was buried in, her name is spelled Banford.