Hi Sarah,
I know that it was a long time ago that you posted this query, if you already have this information I apologise.
Kirtons is an area (in the UK would probably be called a hamlet) in the parish of St Philip, SE of the island. Most areas on the island are named after the plantation that was most often there. Indeed, there was a Kirtons plantation and a good site - Creole Links, states that the owners were : 1796 Edwin Lascelles: 1801 James Nurse : 1826 James Nathaniel Crichlow : 1841 Philip Lytcott Applewaite and 1844 In Chancery.
Regards,
Julie