I think it's really difficult to have a Sub-Saharan state become a great power per se, but you could easily have some stable, independent nations that might avoid colonization entirely.
For example, if one of the various civilizations at Great Zimbabwe could develop a powerful military to back up their economic strength, we could see a solid nation existing there for a long time. Furthermore, if they could somehow gain control over the nearby coastal city states(Kilwa, Sofala), and repel the Portuguese and the Omanis when they try to take them over, then we could have a proper empire based around Great Zimbabwe, wealthy from trading with half the world, and armed with a military potent enough to repel any potential threats. Basically, if you could get Great Zimbabwe dominion over the African coast, and a military strong enough to protect its interests, then we could see a state stable and powerful enough to repel incoming European powers, at least for a while.
Another route you could take would be to have the Bantu migrations start maybe a thousand years earlier, so that their colonization of South Africa and the Cape would have happened faster. OTL Bantu tribes like the Xhosa were unable to colonize the Cape of Good Hope because their crops were incompatible, but maybe with an extra thousand years they would be able to work out a system that would allow them to settle there(With the thousand year-boost, they would likely get to the Cape around 200 B.C, and start settling it around 800-1000 A.D, while OTL they only reached Natal around 1500 A.D). Furthermore, if you could have some kind of great military leader arise around then, we could see Shaka-esque military reforms occuring, making the Bantu military a force to be reckoned with. With this army, the southern Bantu tribes could form an empire(or a number of empires) over most of South Africa, which would make colonization attempts by the Dutch or Portuguese nearly impossible. OTL settlers from Lisbon and Batavia only had to contend with the native Khoisan peoples, who were no match for white firepower, but such a victory against a centralized, powerful Bantu empire with potent military strength would be near-impossible for settlers, and very difficult for even a professional European army.
I would personally go with the second option as the most likely bet for a Sub-Saharan nation that could at least resist European occupation and become as powerful as, say, 19th century Italy. A Great Zimbabwe empire, while powerful and wealthy, would lose everything if its trade networks were destroyed(something the Portuguese had the potential to do). A stable, militarily powerful Bantu nation in the Cape of Good Hope would likely be almost unassailable, and, after repeated failures to conquer it, European powers would likely just lose interest. So if you did go down that road, a Cape Bantu kingdom could remain independent till the late 19th century(at least) or become a decently-sized nation with a moderate share of wealth and power.