I have a book of Abstract of Wills of Edgecombe NC 1773-1856
Cannot give you exact locations of the land, but Ezekiel is listed in this will.'
Apr. 06,1785 August Court. 1785
Wife & extx: ELIZABETH.
Son: JACOB plantation whereon I live, also 75 acres on Whiteoak Swamp (obtained) from my father JAMES COKER. Son: EZIEKIEL, 57 acres on Whiteoak Swamp purchased of Demspey Spier. Also 125 acres of own entry, Oct. 28,1782.
Exxr: Brumblea Coker. Sit: James Boykin, Nathaniel Coker
I know this is not exactly what you were searching for, but it does give you up to the grandfather's name of Ezkiel, in case you are doing genealogy of the family.