So, several people in this thread have mentioned former Portuguese Africa one possible contender. I would like to offer some thoughts on the matter.
It certainly depends on your definition of "white minority regimes." It seems to me that what the OP had in mind was strictly limited to something in the molds of OTL Rodhesia/South Africa, where the white minority was legally put in charge of running the nation and openly discriminated agaisnt the non-white majority. However, for some people here, it seems that a nation where a white minority is simply disproportionately represented in the political/economic elite can qualify as a white minority regime.
If that's the case (and I don't really think this is a very good intrepretation of the term) then it would be relatively easy to get a society like that to emerge in former Portuguese Africa. Simply get Estado Novo reformers to gain control of the government during the 1950s or 60s and you (hopefully) get a slow decolonization process under which Angola and Mozambique gradually gained independence while maintaining relatively large white minorities. Assuming the countries are stable after independence, the political and economic elites will surely be disproportionately white for quite some time.
However, there would be no institutionalized discrimination in this scenario. It's important to have in mind that such a thing runs contrary to Portuguese colonialist ideology, which explicitly sought to create a pluricontinental, multiracial polity united under the Portuguese state, language and culture. This agenda was pursued with varying degrees of commitment throughout Portuguese colonial history. While the "final form" of this ideology- lusotropicalism - was only adopted by the Portuguese state in the 1950s, and still practically ignored until the 60s, it had been the general guiding principle since the early 20th century, at least, and it has in early Portuguese colonial policies (dating back to the 15th century). Integration of native African saw some progress during the 1910s and 20s, then suffered a severe setback at the beggining of the Estado Novo in the 30s, slowly started to gain steam again in the 50s, became more vigorously persued in the 60s (though not always with the best results), and was going at an almost frenetic pace by the early 70s (EDIT: With this, I only mean things were improving much faster than they had been during the previous decades. Not that things were actually getting "good"). By 1974, Angola had arguably achieved color-blind education and was beggining to develop a native elite (EDIT: This was mostly only valid for the cities, though). Also, almost half of the Portuguese colonial forces fightinhg the war against the MPLA and UNITA were composed of native africans. In Mozambique, the situation was never so shiny, mostly because Rodhesia and South Africa had some influence in the south, but also because the Portuguese military and civilian leadership in the area (especially commander in chief of the army of the army of Mozambique, general Kaúzula de Arriaga) was not as enlightened...
Still, the official Estado Novo colonialist ideology was followed there, and most of the people who believed in retaining a white Portuguese presence in Africa also likely believed it to a degree. I know at least a dozen of people who used to live in former Portuguese Africa, and most of them will berate you for even suggesting that there was such a thing as racism in Portuguese Africa during the 70s. I know for a fact that that is not true, but I also believe that it was not their intention to be racist in any or form and that they genuinely believed at the time that the Estado Novo propaganda of a better future for people of all races could be turned into a reality.
I'm not trying to portray Portuguese colonialism as noble or anything. Even considering that most of the 1 million+ Portuguese people living in Africa at the time were not racist, the system was still tremendously unfair for the natives, and it shouldn't be romanitcized or apologized for in any way. However, I do think it's important to have in mind that the concept of "white minority" rule would not find many supporters in Portuguese Africa. Both the colonial populations and the Estado Novo's political and military elites would be sceptical at best, and downright hostile at worst, because it's something that runs contrary to everything they were told they were fighting for.
The only way I can see a system like this emerge in former Portuguese Africa is if Rodhesian and SA downright invate southern Mozambique in the 70s. They could get some (limited) support from ultra-righist Portuguese army officers and some tiny white paramilitary organizations in the former colony, but they would still have to do the lion's share of the job.