Why would one demand an era of peace in Africa when no other continent has really had one?
To your other point, prosperity: Sure. Egypt has had many periods of prosperity. South of Egypt, both Nubia and Ethiopia have had recurrent experiences of empire. Farther south, still, smaller empires speaking Swahili arose in the Lakes region in what is now Kenya and Tanzania.
In addition, the regions where Morocco, Algeria, Tunisia, and Libya are now located have experienced several long periods of prosperity, notably Carthage, then under Rome and Byzantium, and later under Damascus and Baghdad, then with various local kingdoms. Farther south, the empires of Mali, Ghana, and Songhai flourished for many years, (roughly consecutively).
South of that, a number of different geographic features resulted in fewer large cities and, thus, no empires–just as one finds no empires among the pastoral regions of North and South America or Asia, (the Mongols arising at the edge of agricultural China).
Generally, one needs to be able to establish a settled agricultural society in order to promote kingdoms and empires and the native food sources were not sufficient to permit the rise of great empires in the rgions I have named but of which you have not heard. Instead, pastoral societies dominated much of the region–again, much like similar regions of North and South America and Asia.
When the Arabs and Europeans began penetrating farther into Africa, they initiated a slave trade that simultaneously weakened existing kingdoms with internecine warfare while physically removing millions of inhabitants. Later, European colonizers moved in and, while they established infrastructure to support their colonies, they varied between tolerating some local assistance without really promoting it, (Britain), and actively refusing to permit local peoples from being taught anything regarding the infrastructure (Belgium). In contrast, when the Europeans colonized Asia, they found larger kingdoms and empires with an existing civil infrastructure that they employed for their own uses, and the local inhabitants were able to adapt to the European industrial revolution. In the Americas, European colonization was accompanied by disease that destroyed most of the local population so that the colonies were, effectively, rebuilt as a new, Western subsidiary Europe. Africans, having resistance to European diseases, failed to die off, but lacking the strong internal bureaucracies of India, China, Siam, etc., were not incorporated into the European empires in the same manner and far less technical knowledge was transferred to local regions.
When the European countries gave up their colonies, it was the height of the Cold War and several separate, (although interdependent), things happened. The West and the Soviets, vying for power and influence, continually interfered with local governments in ways that prevented serious development. At the same time, socialism had not been demonstrated to be ineffective and many African nations experimented with various forms of socialist economies, probably hamstringing their efforts. And, of course, most African nations had been “put together” by European powers with no concern for previous ethnic boundaries, so many ethnic conflicts arose as groups attempted to secure power for themselves. (This last is hardly an “African” characteristic as a review of the histories of Iraq, Yugoslavia, Ireland, Belgium, and Czechoslovakia will attest.)
I am not sure what “simple” explanation you might reject; the situation is sufficiently complex. Some folks might employ “slavery” or “colonialism” as shorthand for a whole series of situations, but there is nothing simple about what happened.