As many answers have mentioned- the word כושי is a biblical term whick reffers specifically to peoplr from כוש and in general - to black skin people.
When I was a boy, during the 60's and the 70's, there were no africans in Israel and we could only see them in moovies or read about them in books, and the name כושי reffered from our point of view to strange or exotic people from far away whose skin - how strange - was black, or sometimes as nickname for people who had dark skin (for example - yemenite jews).
In the last decades, when the PC rules reached Israel, many people thought that we should change the term כושי with another one, in the same manner the Americans changed the terms negro/nigger/black with "Afro American".
I think it was a very silly step:
1. In contrary to "nigger" which was invented to humliate, כושי is a neutral biblical name.
2. While in USA the above mentioned names which reffered to the color were replaced with name which reffer to the place of origin (Afro-American), the Hebrew PC replaced the term which reffers to the geography (כוש) with terms which reffers to the color (שחור).
3. Racist people have given the word כושי an offensive meaning, in the same manner they have given ערבי an offensive meaning. What should we do now: change the term ערבי with another one? Ask everybody not to mention the English term "Jew" because some antesimists use it as an offensive one?
The bottom line: כושי is an old biblical Hebrew name, not offensive, and I think we should not hesitate to use it.
Cuanto más sé, tanto más entiendo cuánto aun no sé