If you can be flexible on the time of year you travel, then you can take advantage of the low season rates offered by many safari lodges.
These do, however, tend to co-incide with less than favourable weather conditions, so there is a downside - but the wildlife is still about, whether it is raining or not!
In Zambia, for example, the heavy rains fall between November and April; in Kenya, the heavy rains are between April and June; and in Tanzania, between April and May - so the lodges that remain open over these months will offer very good rates in order to attract clients still to come and experience a safari at a fraction of the normal high season rate cost.
In South Africa, the low season rates run from the beginning of May until the end of September, but this is NOT when the rainy season is, oddly enough! Rather, the low season rates in South Africa are linked to when the weather is worse in Cape Town! In all honesty, these months are actually the best time to go on safari here. The winter months of May through to September in the safari areas such as Kruger and Madikwe are the dry months, which means the bush is not as green and lush, making for better game viewing, plus the wildlife are more reliant on waterholes and rivers, so finding the game is easier too in that respect.
Botswana is a year round safari destination, with individual safari destinations offering their own unique experiences at different times throughout the year.
The Etosha National Park in Namibia is another year round destination, but the Park is always extremely busy during December and January in particular.