Have you looked at the Book list?

There are some decent works there, though the list overall could do for some updating.

otherwise, I'll just quote some recommendations I gave to a different source request.

Martin Meredith's the State of Africa (also has the alternate title the Fate of Africa) is a decent introductory overview of the independence era. It is about 700 pages, so rather long, but quite readable.

For a book that accomplishes a similar objective of being an introduction to pre-colonial African history, I like to recommend Roland Oliver and Anthony Atmore's Medieval Africa; 1250-1800, though of course it is limited in scope of time.

Graham Connah's African Civilizations; an Archaeological Perspective is pretty nice as an archaeological overview of the pre-colonial history of the continent, though at around 300 pages, he can't cover every thing. The 3rd edition just came out about last year, and is substantially updated, and he has added information about North African archaeology.

I would recommend the History of Islam in Africa by Nehmia Levtzion and Randall Pouwells, under the rationale that Islam has been one of the major movements that has shaped African history on a continental scale. Levtzion and Pouwell's book is a good introduction that explains rationales for conversion to Islam by Africans, the Islamizing of communities, as well as the Africanizing of Islam in those communities, and the links between merchants, law, and islam.

To supplement the above, I also like Roman Loimeir's Islam In Africa; an Anthropological Approach.

There are a few authors who I really like, like Jan Vansina. His book on Oral History is not per se an account about African history, but it does provide a lot of insight about how oral traditions are formed, the implicit meanings of tropes, and how to include oral history as part of telling the story of a community. Jan Vansina did a lot of work on Central African societies, so that book does contain a lot of illustrative anecdotes about african oral traditions. You should also check out his other work.

I also really like things by John Thornton. Africa and Africans in the making of the Atlantic World is probably his most famous work, but he has written numerous articles about the Kongo Kingdom, Portuguese Angola, cities, religion, warfare in atlantic Central Africa.

In addition to the above, if you are comfortable reading academic literature, you might check out the Oxford Handbook of African Archaeology edited by Peter Mitchell and Paul Lane. It was published in 2013 and contains submissions from leading archaeologists to discuss the historiography and current trends in their subfields. You probably wont want to buy it, because it is 1000 pages and ~150 bucks. Instead, see if a nearby library can get you access.