How might the history of Africa have been different if there had been no Atlantic slave trade?
African Slaves where being sold into slavery by other Africans. Only the strong, young and healthy was captured and sold to the highest bidder. The old, weak,sick and the undesired for purchase,was killed.
The African slaves quickly became the desired slaves over the Irish Slaves, whom had been captured, for the sole perpose of slaverery. Eventually someone had the idea to, (breed) the healthiest and strongest African Males with the healthiest Irish Females. This offspring was sold into slavery at a cheaper price than the Africans but more than the Irish.
It's possible that the stimulus of (other) European trade might have helped some of the Kingdoms develop at least to the level of , say, Persia or Thailand. Strong ans sophisticated enough to play off the European powers one against the other. Modernization was going to happen in any event, and it is seldom pleasant.
The most intriguing aspect of this question to me is that while one can pen a plausible argument that Africa's history might well have gone through a similar series of events, the world would indisputably be a very different place had the Atlantic Slave Trade not existed.
The US, much of Latin America and the Caribbean islands would all have needed drastically different development strategies, and given European nations involvement in the New World this would have had effects on Europe as well.