The CofI Baptism records for Drumcliffe parish held by RCBL go back to 1807, although marriages are only listed from the 1900s. Older marriages for the parish appear to be available in the National Archives
Might be worth checking neighbouring parishes also, in case James was from another parish, or the family moved there after the marriage. There's a map of civil parishes (usually the same as CofI parishes) on the Irish Times website - see : http://www.irishtimes.com/ancestor/fuses/civilparish/index.c...
Given the timeframe, and the fact that they were farmers means it would also be worth checking Tithe records for the area. These date from between 1823 and 1837 (varies depending on the area) and include details in a similar format to Griffith's. These are available, on microfilm in the National Library.