The coal deposits in Palapye are discovered along with the diamonds in Orapa. The British government decides for administrative reasons to combine the Bechuanaland Protectorate with Rhodesia. Mining rights are given to British companies.
What happens next?
Well, I would guess that, like the gold & diamonds rush in Jo'burg and Kimberley, respectively, there would a rush of settlement in the area, so that the area probably becomes rapidly urbanized - i.e. Palapye could have triple the population in TTL, or more, than it has in OTL. This could definitely lead to a boom in the Bechuanan/Rhodesian economy, for sure.
With the combination of the Bechuanaland Protectorate with Rhodesia (question: Southern, Northern, or both?), it would make sense for the then-new settlement of Francistown to become the capital, IMO. Eventually, if the new country decides not to become part of *South Africa, it could thus become a Dominion. Mafeking - the now-old-in-TTL Bechuanan capital - would probably be an exclave of the new country (unless the border with *South Africa ends up looking partly like the border of the old Bophuthatswana bantustan).