The Dutch are the main one (barring a medieval or earlier POD), possessing a large network of forts which with some help and a stronger Dutch government (perhaps also including South Africa and the Austrian Netherlands), they could gain a Portugal-sized empire. Not to mention they had some clashes with Portugal's empire and could perhaps gain both Angola and Mozambique. I guess you could also get Spain more interested in Africa, but their problem was they already had a nice empire in the Americas, plus had the Philippines. And by the time they lost the Americas, Spain was in a pretty horrible state the rest of the century they couldn't just rebuild their empire in Africa since they were too poor to do so. Possibly an early united Italy could do something, but I don't see sub-Saharan Africa being a major priority compared to Europe, although they can certainly match OTL Italy's empire and a bit more.
A German colonial wank in Africa seems possible, if Germany unifies earlier, colonises earlier, and focuses huge efforts in Africa. If they send a bit of their emigration wave to Africa, then they can form the core of a powerful colonial force which perhaps in some Franco-German War (not a Great War) can grab whatever France is trying in Africa and expand these nascent French colonies into proper German ones.
Other than that, you're faced with the issue that while many European countries could colonise Africa in the 19th century, anything more than a small spit of land somewhere isn't going to be possible or politically doable at home. And you'll need some big players in the game to open Africa to European colonisation like England and France did. Other African colonisers is easy. Them doing most of the African colonising is not.
Sicily (and via them, later, Italy). Ottomans and Netherlands, as well. Just don't ask me how to contrive it.
Technically, the Ottomans did colonise Africa, both Eritrea and North Africa, and with the help of their nominal vassal Egypt, conquered down the Nile all the way into the modern Central African Republic.