Any progress on this (know this is years later). I have traced my ancestry to this same John Pinkney Bryant.

Some possible leads (repeating some of what already is said):

1) There's a John Bryant in 1820 Madison County Census
2) There's a Pleasant Bryant in 1820 Madison County Census, he also has a death entry at 1850 which states he was 87 when he died, making his birth year 1763... Could be a father or grandfather (or not related at all)
3) John Briant who married Elizabeth Crocket in Jackson County Georgia the count just to the west. He seems to be unaccounted for in my searches on the web (though I might be missing people who have accounted him).
4) In Elbert County Georgia, the county immediately to the east is a "Bryan" family, a Thomas Richard Bryan (born 1793) who had a son named Thomas Pinkney/Pinckney Bryan. May not be related but I find the shared middle name interesting, in trying to find that Thomas Bryan's tree, I have found no explanation for their shared middle name either.

I'm hoping to get my uncle (a male Bryant descendant) Y DNA tested to maybe shed some light on further connections.