I think the biggest question that needs to be asked here is this:
why does the USA have Congo? It's pointless to hypothesize whether
the USA will be Doubleplus Good and manages to make it the best place in Africa with butterflies and rainbows or whether
the USA could potentially be even worse than Leopold's Congo cough nudge cough not saying that they would be but they would without actually establishing the motivation behind the colonial acquisition.
As that will guide a lot of your answers on quite a few things. Why was it established? For what purpose does it serve? How did the US acquire this interest when, OTL, it had no desire at all for any sort of African territory of any type? As pointed out earlier, Liberia was an independent collection of colonies that declared independence and, eventually, banded together to form what is now Liberia.
Frankly, the only way that the US would even be in the
state to contemplate such a colonial region would be if they had the temperament and desire for colonial ambitions at the time. And, after going through a Civil War that devastated their population (taking a greater percentage of their population of casualties than Great Britain during WW1, when comparing
best case for the US vs
worst case for Great Britain), the US is in no mood for overseas adventures at the time of the Berlin Conference; they need about 25 years to reach the 1890s and begin to flex their muscle. Simultaneously, the frontier of the United States had not yet been settled, so the majority of settler population will be pushing in through that direction as well.
So, as far as I see it, you need a few things to happen.
1. You need the USA to have a direct interest in Africa. If Liberia is a colony (or the various state colonies remain part of their states) there is an interest in the region that might promote American explorers and adventures to delve into the continent; it's certainly the easiest POD.
2. You need the USA to be in a period of expansion, not a period of consolidation, at the time of the Berlin Conference or its alternative. This means that the Civil War is averted, occurs sooner, or is far, far less damaging than it was OTL.
3. You need the USA to be willing to...
modify the Monroe doctrine some, as part of its understood meaning was that the US would not allow any exchange of European territory in the Americas without its consent... and as such, the US would keep its nose out of old-world affairs. Liberia is in the Western Hemisphere, so that can be a "technicality" if it is a US possession, officially.
4. You need the USA to have a reason to go out of its way to counter a European power's claims - as by doing so, the European power might make a play in a region far more vital to the USA (Most important is Continental North America, then the Caribbean, then the Pacific, then South America. And I'm sure there are a few things between that and Africa on the list).
So, my proposal would be:
- Liberia is founded as a collection of state colonies, and instead refers to the region in general, at least at first. Colonization is kept to the edge of the continent, truly intending to be more of a homestead act. The colony experiences horrible rates of attrition as before.
- This doesn't affect the Civil War too much, excepting some increased black immigration from the US to these colonies. It may even become a pseudo-penal colony, at least in some forms. At the outbreak of the war, the various colonies of the seceding states become independent. And, after persuading northern states (Maryland, Pennsylvania) to give up their territory, the region is founded officially as Liberia
- If this is too much to believe, then consider it as a US territory from the start, with the states slowly selling their claims to the US. Works either way.
- In any case, the US takes a much more aggressive stance against the South, and the South starts off on a worse foot (some states don't secede? Perhaps secession is pushed back another 5 years, or more, and the North is even stronger than it would be OTL. or altogether). Within six months, the South is essentially defeated.
- Slavery is abolished through some manner of expedited manumission, and is potentially coupled with a homestead act that applies to the Midwest, Liberia, etc. It is hardly completely successful, but more blacks leave the South than left OTL
- An alt!Congress of Berlin occurs, with multiple powers laying claim to the Congo (Germany, France, Britain, Belgium, etc).
- In order to ensure that no one European power takes it, the Congress deems it into the trust of the US, who has shown capable (to European sensibilities) management in Liberia and has no major favorite.
- It really helps if the US has a slight falling out with the United Kingdom leading up to this.
- The USA starts working to claim parts of the Congo, but doesn't get as much as Leopold does. the French get their piece of Congo, the British get Katanga (as having boots on the ground is far more important, and alt!Britain still would like Cape to Cairo). Other bits are nibbled, but the USA is left with majority of Congo as it is OTL, minus Katanga.
As such, the USA ends up with the Congo, not out of any particular desire for it, but because they are the only ones who didn't particularly desire it in the first place (AKA: the Swiss Solution. Make everyone unhappy). Development of Congo Rubber in this situation
should parallel the Firestone National Rubber Company in Liberia. While the Liberian operation only came to be due to the US's desire to have their own personal supply, the number of alternate suppliers would be lower, and production would certainly start in earnest much more quickly. It depends on the share of the worldwide rubber production that the Congo was responsible for.
As for population comments... I
believe that the Congo lost about half of its pre-Free State population during the time of Leopold's reign. I
think that comes to about 5 million, but I'm just attempting to remember numbers off of the top of my head; I could be wrong.