My wife has a Sigma 50-500 f/4.5-6.3 vibration reduction lens ($1700) which she uses on a Nikon D7000 for wildlife photography. It is reasonably sharp & fast focus and the wide zoom range is very helpful. It can often be hand-held with good results.
That said the Sigma does not focus as fast as my Nikon 600 mm f/4 VR but of course there is a huge price and weight/size difference!
Another option is a Tamron 200-500 f/5-6.3 zoom. It is not vibration reduction but the price ($900) is much less than the Sigma 50-500 and it works fine on a tripod.
We have all of these lenses so I write from first hand experience.
Walt Custer
My wife and I each have a D7000. It is her primary body and my second (to a D3s).
In my opinion the D7000 is excellent. Great features and photos/movies for its price.
Walt Custer
I have been using it for a few years and am very pleased.
see http://waltc.smugmug.com
I use Photomechanic to cull & rate my photos and I can upload directly from Photomechanic to Smugmug.
Walt Custer
Another long lens option is rental just for the time you are in Africa.
See:
www.borrowlenses.com
www.lensrental.com
Regarding weight restrictions (another person's post) we have taken some heavy equipment to the Serengeti as well as other parts of Tanzania and elsewhere (Botswana, Egypt, central America, etc) without issue. Many factors apply including your outfitter's willingness to deal with "excess" luggage and whether you will be taking inland flights in small planes. For large planes (international flights) I have been able to fit my most valuable camera gear in a carryon bag. I check luggage with my clothes, tripods, the bulky lens hoods for my 600 mm, etc and hand carry the bodies and lenses.
The warning about weight restriction is certainly well warranted but thus far (lucky perhaps) I have been able to work around it.
Walt
Sounds like a great trip but I doubt that you will see tigers unless you visit a zoo.
We have been on photo safaris to both Tanzania and Botswana and have found a long lens VERY desirable. If you are shooting from a vehicle either a beanbag or a monopod will be helpful. In predator country it probably will be unlikely that you will be shooting from the ground! Having 2 bodies is nice - one with a telephoto and the other with a shorter, zoom lens. Animals can be anywhere and switching lenses can miss the shot.
See http://waltc.smugmug.com and look in the travel section for our Tanzania and Botswana (both Chobe river and Kalahari) pictures. You will see the value of a long lens.
I have a 600mm f/4 Nikon lens (heavy & pricey). My wife has a 50-500 mm Sigma lens which was much less expensive and still does the job well.
Walt Custer