Given the naming pattern for Mark and Catherine (FAIRBAIRN) DOUGLAS' children, Catherine's father might be a Robert FAIRBAIRN.
A possible candidate for Agnes is therefore Agnes NIVISON, married to Robert FAIRBAIRN in Smailholm whose daughter Catherine was baptized in Smailholm 6 Jan 1799 (known other family Margaret 1796 and George 1801) 
This is entirely speculative, needing more investigation! Henderson-2297 15:21, 13 December 2013 (EST)
Place Lowick, Northumberland, ENG
Notes: DOUGLAS: Mark 35 ag lab b Cty; Catherine 35 b SCT; Mark 14, Agnes 11, Eleanor 8, Robert 5, George 2 all b County; Agnes FAIRBAIRN 80 ind. b SCT 
Place Haggerston, Dist of Berwick, Northumberland, England
Notes DOUGLAS: Mark 47 farm lab b Ellingham, NBL; wife Catherine 48 b SCT; moher-in-law Agnes FAIRBAIRN 92 wid. b SCT; Children: Mark 25, Agnes 21, Robert 15, George 12, all b Ancroft, NBL; Catherine 6 b Chalton, NBL