Cleopatra was not black. In fact, she was not even Egyptian or Middle Eastern. Her entire pedigree of ancestors were of Greek-Macedonian nobility dating back to Alexander the Great's general Ptolemy Soter.
Alexander of Macedon conquered Egypt from the Persians with his Greek-speaking army. He placed Ptolemy there as military governor before he died in Babylon. Ptolemy then proclaimed himself King and Pharoah of Egypt. His capital was the new city of Alexandria. The Egyptians by this point had become a sub-class of peasants who were ruled by the Greeks and the Ptolemaic kings and queens. A Macedonian king in those days would not have married an Egyptian and had heirs by her. Nearly 300 years passed from the first King Ptolemy to the last of the Ptolemies: Cleopatra. She took on much of the style and manners of an ancient pharoah, but was no more native Egyptian than any other European.
The "black Pharoahs" were the 25th Dynasty of Egypt who moved north and conquered Egypt from Nubia/Kush. That happened about 700 years before Cleopatra lived. They were the last of anything close to native Egyptians to rule before the Assyrians conquered them. Since the fall of the 25th Dynasty, Egypt was a territory ruled by foreign princes basically until the British granted independence in the 20th Century.