Ballygowan is in the parish of Killinchy. The following church records exist for that parish, for the era you are interested in:
Church of Ireland. Killinchy (Down diocese) Baptisms, 1819-77; marriages, 1825-45; burials, 1824- 76; vestry minutes, 1716-57, 1779 and 1800-1944; accounts, 1778-90, 1794 and 1809-33; preachers’ books,1824-73 and 1878-1947; printed list of rectors, 1637-1885.
Non Subscribing Presbyterian. Killinchy [Includes records relating to Killinchy Presbyterian Church prior to the setting up of the Non-Subscribing Presbyterian Church in 1835]
Baptisms, 1812-54; marriages, 1813-45 (with gaps); indexes to baptisms and marriages, 1812-54; marriage notice book, 1845-54; pew rent book, c.1785; accounts, 1781-1835 ; lists of names of heads of families and their children, 1841; printed list of stipend payers, 1881-2; typescript history of the church, 1835-1935; stipend and other accounts, 1875-6.
Copies of the above records are held in the Public Record office (PRONI) in Belfast. They are not on-line anywhere as far as I am aware. If you are unable to visit PRONI you would probably need to get a researcher to look them up for you.