Thanks Forfarian however the Blackrigg in question is definitely in Clarkston, near Wester Moffat. It appears on Roy’s Map of the Lowlands, immediately to the west of ‘Moffat’ and ‘Brownyside’.
It doesn’t appear to be marked on any of the Ordnance Survey maps. However, the 1921 Census for Blackrigg Farm places it near Towers Road. The Valuation Rolls and Death Record of David’s youngest son Alexander Shanks in 1921 and his wife Christina (nee. Forrest) in 1923 record it as ‘Blackrigg Farm, Forrest Street’. So it looks as though there were at least two farms called Blackrigg in the parish of New Monkland. This Blackrigg Farm being in Clarkston and distinct from the other Blackrigg in New Monkland near Wattston. It also isn’t the Blackrigg in the parish of Shotts.