There is something mysterious about your information because Ballycastle isn’t in Derrykeighan parish. It’s in the parish of Ramoan. Derrykeighan parish is some miles to the south west of Ballycastle, and there is another parish between them.
As far as searching church records is concerned, you don’t say what denomination that your ancestor was. The Scottish origin would suggest Presbyterian, though there can be exceptions. For Derrykeighan there are Presbyterian churches in Benvarden and Dervock. Benvarden’s baptisms don’t start till 1864 and Dervock’s in 1827. The only Presbyterian church with any records for around 1820 is the Reformed Presbyterian Church for Dervock & Ballymoney which has the following records (acc to the PRONI website): Lists of members by society, baptisms, marriages, deaths and removals including emigration, 1804-44; That would include the period you are interested in. The Church of Ireland’s records for that period were destroyed in the 1922 fire.
For Ramoan parish, the Church of Ireland records for that era were also destroyed in the 1922 fire, save for burials 1805 - 1831. Ballycastle Presbyterian Church records start in 1829. There is also a Presbyterian church in Ramoan but it has no records before 1900.
