The name is mostly spelled Cupples in Co Antrim though there is one Couples in Ballymena in the 1901 census and he is Presbyterian. The name Cupples is very common in the area.
There’s about 20 Cupples graves on the local graveyard site:http://www.thebraid.com/genealogy.aspx
You would need to go through the various Presbyterian church records to try and trace the family. There are 6 Presbyterian churches in the town, and not all have surviving records back to the 1840s and earlier. What records do survive have mostly been copied and are held in PRONI, the public record office, in Belfast. They are not on-line and so you would need to go through them yourself, or get someone else to do it for you.
McCarbery/McCarberry/McArbery as a surname is not common. There are only 1 or 2 in both the 1901 & 1911 censuses for the whole of Ireland; none in the Ballymena area. None on the Braid graveyard site. So again the name may have been spelled slightly differently. It doesn’t seem to be a name local to the Ballymena area. You might also try Carberry as the Mc prefix was often detached from names here. (As was O’).