Again, we cannot make any guarantees but you will have a good chance of seeing the Big 5 at any time of year in Tanzania (of course depending on the national parks you visit).
Elephant and buffalo can be found in Lake Manyara, Tarangire, Ngorongoro, Serengeti and Arusha National Parks.
Lion are found in Lake Manyara (very difficult to find), Tarangire, Ngorongoro and Serengeti.
Leopard are found in Tarangire, Ngorongoro and Serengeti.
Black Rhino are found in Serengeti (very, very, very difficult to find here) and Ngorongoro (probably this is your best bet for spotting a black rhino).