I too have been thinking about this, because the board deserves some sort of Africa-wank! The only problem with my scenario is it makes the USA a nastier place...
In 1831, a relatively anonymous slave named Nat Turner dies, and thus there is no major slave revolt. Without this added fear of slaves, Virginia is more open to the emancipation movement, and by the late 1830's, slavery is banned in Virginia. As time goes by, the split between the North and the South is widened, with more and more pressure mounting on the South to relinquish slavery. Meanwhile, many in the North are turning to Liberia as a solution to the perceived problem of blacks living among them, Liberia being a new home for the blacks in Africa. By the late 1840's the issue of slavery in the South is brought to a boil when Abraham Lincoln* is elected President of the USA, and the Southern States threaten to succeed. However, they are in a far weaker position without Virginia, and therefore more willing to accept Abe Lincoln compromise to buy the freedom the the remaining slaves. By the mid-1850's, slavery is all but gone in the South.
However, this doesn't mean the South has become a utopia for blacks. With no reconstruction, blacks are still terribly discriminated in the South, leading to an exodus of the Blacks to out west, and the North. This is met with mixed reactions; many Northerners were against slavery, but still deeply racists. On the other hand, there are good hearted people, black and white, who open schools to educate the newly freed slaves, who are helped by an already emerging class of educated blacks that came out of the emancipation of Virginia and other 'border' states. Nevertheless, in many areas, the racists feeling prevails, and more and more neighborhoods forbid blacks. In many well-off areas, a more organized solution is found: paying for a trip for blacks to Liberia. In some ares in the deep South, in order to make whites still a large majority, they pass laws requiring blacks to leave for Liberia. Furthermore, a militant black nationalist movement begins, feeling that if the whites won't accept them, they can and will leave for their own nation. This leads to an exodus of educated blacks to Liberia. By the 1860's, the population of Liberia has increased dramatically, with an emerging intellectual class.
While many states and localities are passing laws discriminating against blacks, the new American President decides to take the middle raod as to not upset either party, the racists and the not-racists, by massively funding Liberia. Buy 1870, America faced crisis---war with France over the attempted colonization in Mexico.(Mexi-American war went as OTL) Despite the thinking that America would lose, the military modernization that America undertook after the Oregon Affair with Britain was overwhelmingly successful, and the French leader, facing a uniting German state on his Eastern border, decided a prolonged war with the USA was a bad idea. In 1875, the USA was invited to the Congress of Hamburg to participate in the scramble for Africa by Germany, who was much closer to the USA than IOTL due to their mutual enemy, France. The USA was able to secure large parts of West Africa in order for Liberia to expand.
After a massive population boom and land grab, Liberia experienced a golden age. With their policy of 'assimilation' working moderately well on the natives, Liberia experienced massive growth. However, their was a large amount of tension with their neighbors, French West Africa, due to the treatment of Africans in those colonies. This was exacerbated by French militarism; many French newspapers called for the annexation of Liberia. In 1885, the idea of a "Pan-African Nation" movement was started in Monrovia. However, following further Liberian militarization and some industrialization(aided not in small part by the USA and Germany) the 'Pan-African Nation' became 'Pan-African Empire'.
Ok, I am going to stop this here and ask for input. I think this is plausible for making a successful African nation, but African superpower? Perhaps in the alternate World War One, Liberia conquers French West Africa, and expands, experiencing more growth after the input of oil money. Then, a "Pan-African Movement' is acted upon after Liberia enters an alliance with.....Ethipoia, the Ottoman Empire, and S. Africa? By 1950, far more of Africa is controlled by successful nation states, and a NATO/EU like organization is formed.
Edit: More to work with. Perhaps Russia wins in an alternate 1870's war with the Ottomans and get the straits opened. Then, they make a deal with Ethiopia, giving money in exchange for basing rights. The Ottomans, cut off from Europe, turn to Africa. This could create a much more developed North and East Africa than OTL.
*Or some other guy. I don't know politicians of this era.