Castlegore is a townland of 1245 acres near Kells. You can see roughly where it is using the Griffiths maps. Griffiths Valuation for 1862 lists a John Swan farming there on plot 28, an 11 acre farm. He seems likely to be related to your family. He was the only Swan listed out of about 80 properties.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch
The farm today is probably off either the Craigstown Road or the Whappstown Rd. The on-line Griffiths map for that townland doesn’t show the individual properties but there is a copy in PRONI and also in Ballymena library local studies section which does. So you can locate the farm today if you wish. The Valuation Revision records show the farm remained in John Swan’s name till around 1886 when the farmhouse fell vacant though the land itself was then farmed by someone else. By 1896, the farmhouse was described as in “ruins” and not worth taxing. So today the farmhouse will be gone but you can still locate the land and where the farmhouse stood.
https://www.nidirect.gov.uk/services/searching-valuation-revision-books
There’s a death registered in Antrim town for a John Swan who died 7th October 1885, aged 70. That might be the JS from Castlegore. You can view the original certificate on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
There were no Swan farms in Castlegore in the tithe applotment records for 1835, so either the family moved in after that, or they were living there but hadn’t acquired any land at that point. There were 3 Swan farms in the parish in 1835. They might be related to them. (Though you would probably need DNA to find out). See:
http://www.irishgenealogyhub.com/antrim/tithe-applotments/connor-parish.php#.WGeJqxR2ug0
There’s several Swan(n) graves in Connor new cemetery. It opened around the 1890s. Prior to that most Presbyterians in that area would have been buried in Kells Church of Ireland graveyard (which is open to all denominations).
http://thebraid.com/genealogy.aspx
Connor Presbyterian church has baptisms from 1819 onwards but no marriages before 1845, so you probably won’t get any further back on the family through those church records.