I saw your post directed to Steve Ragin who tried to help me with a Sumter District connection. Regarding John Cannon and Jemima Broughton. Their son David had a son named John E. Cannon who married Martha Mary Stacey, daughter of Amos Stacey and Elizabeth Kearley. Amos was the son of George Stacey who lived on the north side of Hawkins Branch, waters of Sammys Swamp, waters of Black River, adjoining Joseph Pack, Daniel Kelly, and Dr. James Capers in Clarendon County. This land was sold to Col. Richard Manning in 1822. Elizabeth Kearley was the daughter of Josiah Kearley who married (2nd)Sarah Cannnon, daughter of John Cannon and Jemima Broughton.
The notes below may help explain. I got this information from Hub Broughton who I have known all of my life. He researches the Broughton/Cannon lines. The Staceys are married into these families.
In 1807, John Cannon died in Sumter District, SC. His will, witnessed by Sarah Broughton and Abijah Rembert, named his wife, Gemima, and sons, Edward and Nathaniel. Gemima Cannon (1765 SC - 1854 AL), was the daughter of Edward Broughton and Elizabeth Ragan. Gemima Broughton Cannon had three brothers. Edward Broughton remained in SC on the Santee River near the present day Sumter/Clarendon County line. John H. Broughton moved to Greene County, GA. Nathaniel Broughton migrated to Monroe County, AL. in 1816 or 1817. Gemima married Mr. Runnels before 1810 and had a daughter by him. Gemima Broughton Cannon Runnels migrated to Alabama with her brother, Nathaniel Broughton, in 1816/17, and she is listed on the 1830 census of Monroe County, AL. Two of Gemima's children, Nathaniel Cannon and Sarah Cannon Kearley, wife of Josiah Kearley (father of Elizabeth Kearley Stacey) moved to Monroe County, AL. in 1816/1817. Her children, David Cannon and Flora Cannon Nettles, wife of Joseph M. Nettles, were in Monroe County in 1830. David Cannon's son, John E. Cannon, married Martha Mary Stacey, daughter of Amos Stacey and Elizabeth Kearley Stacey. Source: Herbert Broughton, Frisco City, AL.