I think, if you're going to get strong national presences in Africa, the place to look - other, perhaps, than the Mediterranean coastal areas - is East Africa, from the Horn to the Cape. Historically, both Ethiopia and Zansibar were host to large, organised nation-states, and South Africa is an excellent candidate for another, having a perfectly mediterranean climate and plains and valleys for agriculture, and good resource prospects too, with almost none of the endemic disease of the rest of that continent. A successful import of the right crops and domestic animals could catalyze a powerful state, perhaps Bantu or Zulu, very quickly.
Now, between these three areas there is still quite a lot of terrain that boils down, mostly, to wasteland, and there are still many materials that they do not have - so using what precious metals and gems they do have to trade over the Indian Ocean with Arab and Indian states may be necessary, and, even if it's not necessary, will be great for African progress, especially if they can start getting new ideas and innovations flowing from the same place the Arabs got them.
However, if those barriers can be overcome, then a number of recognisable, centralized, competing states with great potential for world significance becomes a real possibility. Historically, the states which did manage to exist in Africa existed in something of a vacuum - their main territorial rivals were incomparatively small or nomadic, similar to the tribes which surrounded the Roman empire (well, the Western empire). Formalized diplomacy, warfare, trade, and competition were not incentivized in these conflicts. Naturally, there were exceptions, but this could be called the norm.
However, theoretically, if proper trade with Eurasia were established, a string of East African nations all the way from Zululand through Ethiopia to Nubia and Egypt, rivals and allies in the same way as historical European and Indian states were, become good candidates for a more European/Indian-style competitive progress. That's the best that can be aimed for, since a single China-style empire just ain't happening. If those East African Empires were established, Western Africa might be colonised, made into satellite or resource outposts (perhaps even for slaves, as historically?), or even progress as well, and existing states there, such as the Songhai, might even be able to grow stronger by alternatively being clients to and playing off European and East African influences (though they're more likely to be torn apart. Still, I want to see a syncretized Zulu-French empire on the Volta!).
Now, these are only a few half-baked ideas, but I can see an obvious potential there. There's a reason why even today the East African states are among the best African states, besides special cases like Botzwitzerland).