I’m not sure what the question is. As recently as 1945, there were only four recognized independent nation-states on the entire continent, the rest of the entire region being held by European colonizers. If you set some limit of “100 years” to achieve stability, then we wind up excluding the whole area by definition.
(By that definition, you can also exclude Russia (two complete governmental overthrows in fewer than 90 years), China (multiple exchanges of “who holds power”, the most recent fewer than 60 years ago), Germany, etc. (And what about the European nations that were held by either/both the Nazis and the Soviets for significant periods within the past century? Do the Czech Republic and Slovakia count as stable or “not yet stable” as neither existed 100 years ago–or, as identifiable nations, ever.)
If you use a slightly less rigid formula of “who permits changes of power by election at this time where no significant active rebel movement threatens?” you can add, at least, (off the top of my head), Ghana, Niger, Nigeria, Cameroon, Tanzania and Zambia (where the “unrest” is of the Mexican “dominant party” variety of politics, not carried out in revolt), and with Angola inching up on the outside.
In fact, I think it would be easier to name the clearly (potentially) unstable countries: Chad, Sudan, Zimbabwe, Congo (formerly Zaire), Liberia (stable but suspect), and Sierra Leone.
Then, there are countries such as Cote d’Ivoire where unrest, while recent, has not been a traditional part of their otherwise stable tradition or Mauritania, where there are ethnic tensions in a single-party state, but where there has been no serious disruption in over 20 years.
As I said, I’m doing this by memory, so I have not included every country (and may have faulty recollections of some situations). If you want to check out one perspective of each country, the CIA’s World Factbook 2002 allows a quick glimpse into each nation’s politics and economy.