Given how only one African state avoided being snapped up in the scramble for Africa(unless you're inclined to count Liberia as a second), I was pondering how to minimize said snapping up as much as possible.
Most of the African colonies were financial drains, snapped up only due to a desire for imperial grandeur on the part of France/Germany/Italy so as to make up for their minimal imperial claims outside Africa, and because Britain felt compelled to compete with them. It seems likely thus that Britain would not have undertaken such imperial expansion without outside competition. Solution: leave Britain the only substantial colonial territory holder in Africa.
ASB? I see a way for it to be so- have Napoleonic victory in continental Europe. This thread
discusses the mistakes he made, and it seems consensus that he could have won the war in Iberia if not for a few missteps. This would mean that Portugal, Spain and the Netherlands are all under French control, which means their colonies remain under permanent British control(as would France's colonies).
I think this is a pretty firm path to keeping most of Africa free of European control. Britain would have zero interest in interior Africa without being prompted by competition(with the possible exception of the Congo which would possibly end up being exploited by some corporate imperialists if not Leopold). They'd probably have concerns about a possible French capture of Egypt and building a Suez canal, but beyond that I think we'd see an unmolested interior Africa.
Whether this would be substantial improvement is debatable judging from Ethiopia which is not notably better off then those African countries that were colonized, in fact Ethiopia is poor even by African standards. So just how would an Africa that predominantly avoided colonization look? Would the interior being undergoing a process of Japan-style emulation and modernization by 2010, or rather immune from outside developments? I suspect for one the indigenous slavery slave trade in Africa would somewhat stronger. On the other hand the arbitrary borders and brutality of colonizers would be avoided.
Edit: On consideration this scenario probably doesn't stop the situation with English colonization and Afrikaner expansion in Southern Africa- their were already Europeans there, and their's still going to be gold in the Boer territories. Though I doubt they bother to expand their military presence into the Botswana/Zimbabwe area, let alone any further North, given the lack of German and Portuguese expansion inwards.