Black is absolutely accepted as an accepted adjective. Especially with the capital-b, Black is used to refer to the unique Black culture and heritage in the United States. Black history is one where people were taken from their nations or places of origin, transported to a foreign land, and put in bondage. As you say in your own comment, many black or African-American people (whichever label you prefer) have little connection to Africa; it wouldn't make sense to them to refer to them by nationality or origin, when Black culture is its own thing.

Don't get it twisted: I agree that the history of African-Americans in the US is one marred by slavery, segregation, racism, and the constant struggle to attain and retain equality. But out of that came something unique that many black people celebrate to this day.