Wow, two days notice! My educated guess is that unless you find a coupon before tomorrow, you are probably stuck with what you have already found.

Actually, needing to take it in the morning might be a non-issue, because depending on where you are going in Joberg, there are several pick up locations right in town, and by picking up in town, you will probably avoid the daily airport pick up surcharge (might be a $2-4 per day) as an add on to the daily rate (meaning 30 days could add $60-120 in airport fees for the rental, over and above the rate), but this only applies if there are car rental airport fees for ZA, since all countries are different, and I have not yet been to ZA.

However, if the cost of transport into Joberg is over $60 (depending on what the airport fee is per day), then this might not be a savings, but the return at the airport is not an issue, because Avis usually allows city pickup with return to that same city's airport at no extra charge. This also gives you some flexibility, because if you are only traveling within a 3 mile radius (meaning 3 miles in any one direction) of your hotel for the first few days, you could probably save some money by not renting the car for the first few days or paying for garage parking at your hotel. Then when you do need it, you could get it right in Joberg, such as at the Hyatt, which has an Avis rental location in it or next to it.

Hunt around for coupons, including calling Avis customer service (800-352-7900) and asking them, also checking the Internet, and asking your friends or business associates in ZA to be on the lookout too (asking your friends might not be much help because you leave so soon).

Just on a quick check for time of day, I found a couple of variations for dates which were a bit further out, but that was before I knew your arrival date, since it is so soon, their inventory is probably already baked into the cake, so time of day will not matter in this context.

Rates/day do not always go down with longer rental periods, sometimes shorter rentals actually yield lower daily rates, it depends on their volume and inventories, meaning if they have a huge bunch of weekly reservations for $300/week, they will not want to rent for 30 days for even $1,140 ($2/day less over one 30 day month), because they will lose out on the income for the extra two or three days per month, plus lose out on the extras (if you don't take them), such as PAI and GPS (which is HUGELY profitable). Other times, they might have lower demand for weeklies, so it would be better to rent monthly than to have their cars sit unrented. Also, as we all know, sometimes rates for cars, or hotels, or air, can seem irrational or counter-intuitive, although to the travel companies, they make perfect illogical sense!

(emphasis mine)

I was only asking for the bold part above.

I would guess this totally depends on time of year. When did you go before?