I'd also vote for the Nikon 80-400 VR. I took mine to Africa in 2004 - it had been a gift from my wife the Xmas before. I was very happy with what this lens could do with wildlife, also with it's very reasonable weight, size and cost. You really can hand hold this lens at 400, though a monopod helps. (I didn't have a monopod then, and so ended up using my tripod configured as a kind of bipod in the safari vehicle, which worked well.)
The midday light in most parts of Africa is very bright and lasts a long time - you shouldn't have any problem getting fast shutter speeds at normal ISO levels during most of the daylight hours. If you happen to run into a great action sequence requiring very high shutter speeds in the early morning or at dusk, then you might wish you had a 2.8 lens, but you'll still be able to get a reasonable shot by kicking up the ISO. When the animals/birds you're shooting are stationary or moving slowly, as is usually the case, there is no real problem.
All these were shot with the 80-400 VS, either handheld or propped on a tripod used as a monopod.

Cheetahs

Terrapins

Burchell's coucal
Frogfish (Robert Delfs)