Capenheart 'Coatsworth' Pinckney Black, Sr.
I believe we can rule out John Black and Montgomery. There children don't line up with the DNA matched siblings of Coatsworth. I have also seen it said Coatsworth father was half Cherokee. Im not convinced that Francis Pinckney belongs in this family or to this generation. The only records I can find are civil war Era for a John Black and Francis Pinckney. We are not decdants of Chife Blackfox he was probably only 9 when Coatsworth was born. There still may be a Cherokee connection but it's not 100% fact yet.
I don't see anything that would suggest that Coatsworth/Pinckney had any Cherokee connection. If he was born in 1798 he should have been living in the Cherokee Nation 1835 and be on the 1835 Cherokee census. There is no one named "Black" on that census. The Cherokee didn't live in Missouri. Those who were Removed lived in Indian Territory and those who remained were in North Carolina, Georgia, Tennessee, and Alabama. The Cherokee people were enumerated on rolls in 1851/52 and no one named "Black" on those either. He appears to be living in Marion, Illinois in 1830 and 1840, both before and after Cherokee Removal.
None of these people has anything to do with Chief Blackfox, who died in the Cherokee Nation in 1811 and had no known descendants.