Hello Bonza,
There is a gravestone for a Margaret Cockfield in Dirleton Churchyard. The stone has been erected by her son William.
Margaret Cockfield, his mother died 11 May 1887.William Aitken, his father, died 6 Feb 1886.
Son William died 23 June 1900, his wife Georgina Spence died 19 Jan 1894, his son, John died 15 July 1898. Son William's grandson is also mentioned died on service at Basra, Persian Gulf, 18 July 1916 aged 17 years.
Had a look at her death cert on SP. She was 77 years old (would match with what you posted for Margaret's birth) living at the Distillery, Haddington. However father is David Cockfield, House Painter , deceased. Mother is Janet G???(unreadable). Informant was Robert Watt, son in law.
Also looked at census and she gives her birthplace as Haddington. Although died at Haddington, all census results show living at Dirleton. 1841 census shows father David staying with Margaret and her husband William. Surname for William has been transcribed as Althen, not Aitken.
Also there is an Edward Cockfield, retired painter, born Haddington about 1794 on 1841 and 1851 census - could this be a brother? Probably some relation as he is a painter.
As you say the name is unusual, so there probably is a relationship between your John and Margaret.
Mags