I am also researching Capt. John Koonce who (I think) is of Craven County, NC, because his daughter Aseneth married a Richard Hart from there, and I believe the families migrated together.
Here is what I know: Capt. John Koonce, Jr. is married to an Elizabeth, and their daughter, Aseneth Koonce married Richard Hart in Davidson County, TN in 1808. They became residents of Maury County, TN until about 1846, when they moved to Marshall County, Mississippi.
I hope this helps you out... and any help I can get from you in return would be great!!!