Actually we do. In particular when it comes to St. Gelasius I, who was the Pope from 492-496. The other 2 are from Africa, but their exact race is not known since the Vatican simply states they were 'from Africa.' But St. Gelasius was what you referred to as 'negroid.' He was black, and a Roman citizen (race was not as important as being a citizen of Rome).
Here is some more info on him:
Born in Rome of African decent. He instituted the Code for the uniform ceremonies and rites. Because of his charity he was called the "Father of the Poor". He maintained the supremacy of the church over the kings. He inserted the "Kyrie Eleison" (Greek for "Lord have mercy") into the Mass.
Anyways, that is for St Gelasius.
Moving on to St. Miltiades, who was Pope from 311-314. Church history says he was from Africa, which could mean he was white born in Africa or African born in Africa. Anyways, here is a painting of St Miltiades.
Moving on to St Victor, who was Pope from 189-199. The Catholic Encyclopedia states he was the "Liber Pontificalis" and a native of Africa. This is the one that is most ambiguous. He could be a White Roman citizen born in Africa, or a Black Roman citizen born in Africa.
A black Pope would be cool. The Popemobile would be a modded out '78 Monte Carlo.