Looking at the 1831 census, there were 2 Barr households in Cumber Upper:
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Tirkeeran/Upper_Cumber_Half/Burn_Upper/2/
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Tirkeeran/Upper_Cumber_Half/Tullintrain/27/
One headed by John in Tullintrain had 2 males, the other headed by James in Burn Upper had 6 males and 5 females. All were Presbyterian which fits with your understanding of the family’s Scots origins.
Tullintrain still exists. Burn Upper I cannot locate. The name has apparently fallen into disuse.
Looking at Griffiths Valuation (1858) there was a William Barr in Tullintrain, Samuel & Archibald in Gilkyhill and Major Barr in Lisbunny.
https://www.askaboutireland.ie/griffith-valuation/index.xml
Possibly one of those families might be connected to yours.
Unfortunately the local church records do not go back far enough for you. The local Presbyterian church (Cumber Upper) has baptisms from 1827 and marriages from 1834. (Copy held in the Presbyterian Historical Society in Belfast.)