Barber family of Glenwherry, County Antrim, Ireland.

It looks as though the Clatteryknowes Barber/Barbour family had left by the time of the 1901 census:

https://www.census.nationalarchives.ie/pages/1901/Antrim/Glenwherry/Clotteryknose/

James & Martha had evidently retired and moved to Belfast, around 1899. Neither had married so seem unlikely to have left any descendants. Their mother Mary Jane died in 1891. She was replaced by her son James who took over but he is deleted from the Valuation records in 1899 (and replaced by a James Farquhar). James Barbour seems to have been the last on the family farm.

https://www.irishgenealogy.ie/files/civil/deaths_returns/deaths_1891/06074/4732060.pdf

I widened the search to everyone in the Glenwherry electoral area in 1901 but there were no Barber/Barbours living there then.

James & Martha in 1901:

https://www.census.nationalarchives.ie/pages/1901/Antrim/Cromac/University_Street/971999/

The Barbour family were evidently Presbyterian and so are likely to have attended Glenwherry Presbyterian church. It was established in 1825 but has no records before 1845. Prior to 1825 it appears that families in that area were attended to by the Minister in Ballyclare. Unfortunately neither of the 2 Presbyterian churches in Ballyclare has any records prior to the 1830s so baptisms and marriages conducted in the 1700s and earlier are likely not recorded anywhere.

Information on Glenwherry Presbyterian church attached.

Possibly DNA testing may be a way of matching with others who have additional information about the family. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.

The North of Ireland Family History Society is running an Ulster DNA project and can offer FTDNA testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).