We have a letter to William Douglas from the Presbyterian Minister George Steen MA, and the people of 2nd Limavardy Presb Church, written in 1860, just before the family departed for NZ. William was held in high regard. There is a mention of a recent revival. I think the church was too recently established for the children to have been christened there (the youngest was Mathew Turbitt Douglas b. abt 1856), but they may have been on a membership role of some kind.
The recent revival mentioned is the Great Revival of 1859.
Second Limavady Presbyterian Church dates from 1845 (George Steen was 1st minister). Some of the church records are on microfilm at PRONI (and Coleraine Library): marriages 1845-1904. No mention of baptisms on the roll.