In Africa, no, any states that existed were too isolated to really follow the model.
Egypt did modernize and industrialize. Yet at the same it played so hard that ended up selling itself.
Morocco since 1500 can be described as something like an 'African Meiji Thailand'. It did modernize and kept its army more or less to date with foreign weapons and advisors, and played several powers against each other with relative success. The problem is that its geography didn't allow the population necessary to become an industrial powerhouse, nor to have a firm control over the whole country. And, obviously, the fact that by 1900 the key European nations (Britain, France, Spain) agreed to carve Morocco and the Moroccans couldn't bring others able to play against, despite their attempts to court Germany and the USA. Having a teen king in the crucial 1894-1904 period didn't help, also.
Ethiopia did progress very well with help from the French and the British. It basically went from little more than a tribal chiefdom to a true independent African empire. Obvious problems: They started from a very low level (unlike Japan) and the geography didn't favour them (like Morocco). But they did a titanic work with an astonishing success in OTL. Who could think in the 1880s that Ethiopia was going to be a member of a League of Nations 40 years later, on par with any European nation?
I'm pretty sure that there is one POD out there, not too difficult, to make any of these nations
more successful than they were in real life (because it is obvious to me that they were successful in some way, compared to their neighbours or how bad themselves could have ended).
Less evident but also possible African Meijis could be the Imerina Kingdom in Madagascar and a surviving Mali Empire that wasn't destroyed by the Moroccans in the late 1500s and its legacy erased by centuries of infighting.