Would this thread have been in Post-1900, I would have said it could possibly happen after the 1970's and more likely with time.
In Pre-1900 though...
It should have been before Islamic invasions, as afterwards, Christianity becames essentially an european religion from one hand (yes, I know, you have african churches but they weren't in connexion with Rome); and papacy became largely tied to italian or western european politics (even if it did had an idependence at several points).
Black saints aren't unheard of as Saint Maurice, but it's likely a medieval exoticism.
Eventually, if Roman Empire had deeper ties with Subsaharian Africa (something towards what Arabo-Islamic North Africa had), you would have better chances to have blacks individuals or even groups christianised within the empire.
Of course from that to having popes is still a gap, but it's a necessary foundation.