Agreed with the above. There would be no point for such an activity, and I doubt the political will could be drummed up even if agitated for. It's their country as well. After just going through a war and shedding so much blood to free them, why would the political party in power turn around and kick them out?
If any colony is established in Africa, and it manages to remain in the US for whatever reason, there will be a separation between blacks born in North America and those in Africa. There would be two separate identities between the two.
How to get there? There has to be a US interest in colonization. After the Civil War IOTL, there was no interest for overseas adventures. The US was focused on internal expansion at that time and recovering from the war. See the North Borneo lease expiring: The US had no desire to pursue a colony in its own backyard, much less one in Africa in terrain that would be just as inhospitable.
I think that for this to actually occur, the US would have to have a POD before or during the Civil War. Limit the casualties and the destruction inflicted. If the North Borneo lease is acquired at about the same time as OTL, the US would have a few years to drift into peace and expeditions may be mounted to actually make North Borneo a colony. If that takes place (big if), and the US takes an outward looking viewpoint along with continuing to maintain the Navy at higher standards (after all, they have to defend that colony somehow.
Then, after that, you have the Spanish-American war start early (disputes over the Sultanate of Sulu's territory?) roundabout 1880. And, with that, the US somehow manages to get ahold of Equatorial Guinea in the peace deal. There are a lot of long odds in that entire sequence. The other option is that, after beating the Spanish, the US is seen as a respectable power that could at least serve as a neutral buffer between two other colonial powers? I doubt that would happen; the US has little interest in European affairs at this point. At best they'd take on the role of Belgium or something similar.
In the end, Africa will be an afterthought to the US. Their focus is on the Pacific. Any claims they do have in Africa would probably exchanged for concessions in the Pacific. The only way it wouldn't work is if such a deal fell through. If the US tries to trade Equatorial Guinea for, say Samoa, later on (Or Kaiser Wilhelm's Land, but that would take something far more substantial) and the deal falls through, the US would end up with a commitment in Africa. But I'm not sure whether that would work or not.
Edit: Another idea. Say that the US does go through an earlier Spanish-American and somehow manages to get the rights to Equatorial Guinea in the resulting treaty. That would probably imply that the original Treaty of El Pardo borders for Equatorial Guinea would apply. That would overlap claims with Great Britain and France - Additional points of conflict for both. Just tossing it out.