How could India?
How could China?
How could Africa?
-India:India is easy.... Mughal empire survives, an idea shamelessly stolen from Tony Jones.......
Most Indian states were at a European level.... their only real disadvantages were military, in that they had no real naval power and that they focused far too much on artillery....
So IMO, even if the Mughals collapse, you just need the Indian states to reform their military so that they are more well rounded(their artillery was arguably better then the European artilleries, but they focused on it far too much). Maybe more emphasis on adopting certain Eurpean ideas....perhaps Myosore would be a candidate, indeed it would not be too difficult for it to become equal or superior to the European armies, at least those present in India. I could very much see it becoming an Indian Prussia.... perhaps deliberately following Prussia's model.
Sends a few missions out into Europe, reforming the political system(I'm not sure if Myosore would have any of the problems outlined by TallwingedGoat, or even needed significant reform). OTOH, this may work against them, seeing as they will likely be taking advice from the OE

.
The Sikhs also very nearly managed it.
-China:This may appear a step in the wrong direction to some people.... but I feel a early fracturement of the Chinese state, perhaps around 1750-1800, is the way to go. It would force the Chinese to compete and reform, as opposed to stagnating in their own feeling of total security.
-Africa:Egypt is the prime cantidate....perhaps having them emerge victorious against the Ottomans, seizing all of Syria, would do it. Couple it with de-facto Russian vassalization of he OE(which very nearly happened OTL), and the Western powers have very little choice but to buff up the Egyptians so as to be capable of blocking Russian interests in the area.... much like Britain did with Japan OTL...
So, massive military reform and the establishment of a semi-powerful navy....as well as the Suez canal being an
Egyptian possesion. And if the Western powers became hostile at the prospect of a semi-great power controlling their main trade route, the Egyptians will cut of the trade route

....and lean into the Russian sphere of influence....
Anyway, the Western powers have buffed up the Egyptians into a true military power, capable of engaging, and perhaps defeating the combined might of the OE and Russia (in a defensive war in Syria, that is), and the political system has been fullY reformed....perhaps the Sultan begins encouraging Arab nationalism, seeing hwo events are playing out in Europe, much like NasseR would do 100 years later in OTL.
The economy might be a weak point, as I'm fairly certain that the Egyptians would have a similar problem with industrialization that the Dutch had-they are dependant on a water way. Still, perhaps they could exchange free passage to the Western powers in exchange for yearly lump sums and aid in regards to industrialization. The Egyptians will also gain a boost from the ACW if it occurs, perhaps forbidding the passage of Indian cotton through the strait also, so as to fully domiante the market.
This, of course, needs some luck to begin with and a string of competent sultans....
a Meiji-style revolution couldn't really happen anywhere until the industrial era, at which point India is too far gone. the weak, conservative Marathas dominate much of the continent, and I really can't see them pulling it off.
The Marathas? Conservative?....IIRC, they were the only Indian people not to follow the caste system.
Disunited india that was pretty much dighting themselves when the British invaded. Pleassse....they were too busy fighting themselves to think of new technology that could improve their lives.
In Africa, no, any states that existed were too isolated to really follow the model.
More aggressive Europeans early on then, might do it, causing India t opull together t odrive the Europeans out.
The Barbaray states and Egyp were not isolated, and the Kongo state was both Catholic and had been exposed to European trade for a long time.
On that note, a Zanzibar state(if the OE was rather stronger then OTL, for example, they may back it as a means of gaining influence in the Indian ocean) and a Zulu-wank(especially if it is the Dutch who hold South Africa) are both plausible.