This is actually not terribly hard to do. The Congo was prosperous and industrializing in the 1950's, and without deliberate destabilization by Belgium and the Congo Crisis, could easily have continued on that track.
In The Anglo-American Nazi War Congo is a analog of the Asian Tiger economies, with Congolese-made cars appearing on the U.S. market in the 1990's (it's sort of a Korea to Brazil's Japan). Like OTL, there's lots of European immigration in the late 40's and 50's, most of it non-Belgian. Because Belgium is Nazi-occupied, the Belgian exile regime in Congo is a U.S. proxy. When Belgium is finally liberated in 1960, neither white nor black Congolese are interested in returning to being a colony and Belgium can't stop its independence. I don't know if you need a full Nazi victory, but you need a situation where Belgium is in no position to undermine the Congolese regime and white settlers in the Congo have more connection to the Congo than to Belgium. The second is relatively easy because only a minority of whites in the Congo were Belgian. Allow a ruler like Lumumba to take office instead of a Belgian puppet like Tshombe or a corrupt strongman like Mobutu and there's no reason the Congo needs to be a basket case. Race relations will have to be handled gently and the white Congolese can't be in a position to dictate policy too much, otherwise they'll vote to ensure their supremacy at the expense of the country and you'll have a Zimbabwe situation. The whites need to be an unprivileged minority but whoever runs the country has to know better than to use them as a scapegoat as happened OTL.