Yehudayona, it is a machloket Rishonim if a cohen can marry the daughter of a ger and a gioret. The Mechaber paskens (Even HaEzer 7:21) to be machmir l’chatchila. This even continues for several generations (e.g. son of ger and gioret who marries gioret) until one parent is a Yisrael. Of course, if a black convert would marry a Yemenite or Malabari Jew the daughter would be black and eligible to marry cohanim according to all opinions and then there could be a black cohen.
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