O.K. Alison- There's a James Griffin at a place called Ballindrum, parish Artrea, a hop, skip and jump from a William Griffin, William Carleton and Maryanne Mitchell at Mawillian Townland , parish of Artrea. I can't find a townland map, but the reason I think these 2 places are near to each other is beacause James is on page 289 G.V. and the rest on 290. with 2 very small townlands in between.
Also bear in mind that there were only 12 Griffin head of households in Londonderry at that time, and Mawillian was the only place I could find a Griffin /Carleton match. Mitchell was a bonus.
Do you have the occupation of James? If he was a schoolteacher/caretaker it would be brilliant as he is living next to the school.
However the marriage of John griffin and Jemima Carleton in 1859 is on
http://www.irishgenealogy.ie/
Now it doesn't say if this is a parish or civil record, but if your ancestors were protestant and this is a civil record , you can send for it, and hopefully it might clarify things.
You could send for it from
http://www.groireland.ie OR
click on the following link, then District Register Offices and then e-mail the Magherafelt office and ask if they have the marriage records for Moneymore. (though they may not have married there!!)
http://www.groni.gov.uk/index.htm