I have a pamphlet somewhere entitled “The Five Negro Presidents of the United States.” I bought it nearly 25 years ago on 125th Street in Harlem. It was a cheap, xerox copy of a self-published book with President Harding’s face on the cover. I wish I had it handy now. Such fun!
Harding was a descendant of Anthony Janszoon van Salee, a Dutch pirate and early settler, who was said by some to be Muslim, and others to be Black. The first is possible as he spent time in North Africa and had a Koran, the second is unlikely. When people say Harding was Black, though, they're thinking more about runaway or freed slaves who made their way to the Midwest in the days of early settlement.
Coolidge sometimes get classified as black, but that seems to rest entirely on the fact that his mothers maiden name was "Moor" and moors were supposed to be black. Still, Coolidge did believe his mother was part native American, so maybe it's possible she was also part African-American.