If you’re trying to describe a person with dark skin, well, how about ‘person with dark skin’? Or ‘dark-skinned person’, if you want something shorter, similar to red-haired or one-legged or whatever else you use to describe someone’s appearance.
If you’re trying to refer to a cultural group, then the best word to use obviously changes according to which group. Here in the U.S., I think ‘African-American culture’ is pretty accurate, accepted and neutral. Obviously, if you’re referring to people living in London of Jamaican culture, then ‘Jamaican’ would be a better description. Other cultural/ethnic groups may have their own preferred words they’d like used to describe them, but of course it varies.
‘Black’ is not a very useful a word, because it doesn’t distinguish between skin color and culture. There are a lot of dark-skinned latinos where I live, who have very little connection to African-American culture.
(and in English, at least, the word ‘black’ tends to have all kinds of other associations with evil and badness, making it kind of unsuitable for neutrally describing someone).