Many Presbyterian church records have been copied and are held in PRONI Belfast, on microfilm. Some have not been copied, and these are usually either in local custody (ie still held by the church) or with the Presbyterian Historical Society in Belfast. The PRONI website usually says where they are. Though many Presbyterian churches were built in the 1600s, many of their early records have been lost, so there are plenty of gaps, and not many congregations still have records prior to 1800.
Presbyterian church records are mostly not on-line, and you may need to research them in PRONI (or wherever they may be held) or get a researcher to do so for you. You can see what records exist on this link: