Index to civil registration (online on LDS Pilot site) only goes up to 1922 for Northern Ireland unfortunately).
Marriage certificate for Elizabeth (Baxter) Barr should list her father's name and occupation but meantime here's Baxter baptisms from Macosqun Presbyterian Church (1830-1841) just in case you are able to make a connection sometime:
Children of Benjamin & Margaret Baxter, Camus-
Joseph bapt. 15 Sept.1830
Joseph bapt. 1 June 1833
James bapt. 13 Aug.1835
Robert bapt. 22 Dec.1837
Peggy Jane bapt. 15 Nov.1839
Children of James & Anne Baxter, Camus-
Mary bapt. 24 Apr.1834
Martha bapt. 23 July 1838
Joseph bapt. 23 Sept.1841