Hi cousin Patricia. We are 8th cousins...and around here, that is pretty close!
I ran WikiTree Sourcer, chose FamilySearch and I found a William Johnson married to Elizabeth (Jones) Johnson married 09 April 1821 with 7 children, one is William Johnson.
This sort of looks promising. But they show slightly different birth dates than you show and no death dates or locations. Family Search also hits a brick wall as no parents are listed.
The children are born in England, all with the Johnson name, not Johnston.
Is listing his birth name as Johnson and current name Johnston messing with the search? 
William Johnson 1801
FamilySearch "About" Page
Family Search "Details" page
Family Search "Sources" page with 16 sources
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Elizabeth (Jones) Johnson 1804
Family Search "Details" page
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The Son: William Johnson born 21 Oct 1831
Family Search "Details" page