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.
If I remember correctly (I'm recalling the pamphlet from 20+ years ago), the author devoted much ink to Lincoln but really went to town on Harding.In every instance, the "evidence" came from detractors, political enemies, and hostile journalists.
The last chapter in the book is very cryptic as it contains references to a then living president. I assumed at the time it was LBJ he was alluding to. The author died in the 1960s.