Why wouldn't Hogwarts have black people? Can black people not do magic? I don't see why Hogwarts would bar someone based on muggle affairs such as racism.
World lore black students would most likely attend Uagadou school.
Hogwarts School of Witchcraft and Wizardry - For students from Scotland, England, Ireland, Northern Ireland and Wales - Founded late 10th century
Uagadou - For students from All of Africa - Founded pre-11th century
Castelobruxo - For students from All of South America - Founded 10th or 11th centuray
Beauxbatons Academy of Magic - For students from France, Spain, Portugal, the Netherlands, Luxembourg and Belgium - Founded pre-1290s
Durmstrang Institute - For students from Northern and Eastern Europe, willing to accept international students - Founded pre-1290s
Ilvermorny School of Witchcraft and Wizardry - For students from All of North America - Founded Early 17th century
Koldovstoretz - For students from Russia - Founded Unknown
Mahoutokoro - For students from Japan - Founded Unknown