You're challenge, should you chose to accept, is to create a POD where the Boers win the Second Boer War. The gist is that they maintain their political independence, but anything beyond that is fair game too, but bear minimum they must remain independent states (or create one Boer republic) and you can have a POD as far back as 1880 to work with.
Go!
1) In the very beginning of the war in October, 1899, have the Transvaalers take and hold the railroad bridge over the Modder River. This cuts off Kimberly, Mafeking, etc. No need to siege either...let them wither and die. Set up strong defenses on the north side of the Modder River. Let the British Army do what it is (was) best at... getting its infantry killed due to foolish and incompetent commanders.
2) In the Natal, hold the lines along the Tugela River and let the British Army CO's do what they do best (again [see # 1 above]).
3) Big, tricky & sneaky...have the Orange Free State remain
neutral as long as possible. The terrain of the O.F.S. is notoriously flat and conducive for cavalry & infantry operations. By remaining neutral for several months or (preferably) more, it forces the British to either continuing head/face first into Boer guns and rifles in the rugged terrain of Natal. In the West, the Khaki-coats have to go into the desert to try to circumvent the Boers and try to drive north through very inhospitable terrain on their way to the Z.A.R. (Transvaal). This would cause many more casualties and perhaps lead not to a military victory for the Burghers but a political victory since the British will hopefully grow tired & disillusioned leading to a collapse of one gov't after another. May lead to a negotiated peace on Afrikaner terms.
4)
If the British unilaterally declared war on the neutral Orange Free State, for whatever reason they can come up with, it makes Britain more of the overt aggressor in the public/international eye...leads to more dissatisfaction & social discord within Britain, and more importantly, possible German/Franco intervention due to Great Britain declaring war on "neutral" Orange Free State.
My 2 cents,
Joho .