What Africa needs is locals to spread their own scripts--basically an African Sequoyah (and I don't mean the Vai syllabary which was created from influence by former slaves owned by the Cherokee). The best places would be the non-Muslim parts of Africa, since the more Muslim-influenced parts can use Arabic. Ideally there would be no Scramble for Africa and instead Europeans would stabilise a variety of states in Africa which would naturally use what they know--Arabic--to write their languages. The non-Muslim parts would use a variety of constructed alphabets based on European alphabets, Arabic, and even Cherokee syllabary to write their language, which would spread in various contexts and eventually be used by European missionaries and colonial administrators as a cost-saving method.
NOTE: While I want to screw both generally, if the choice is nothing but latin vs cyrillic, choose cyrillic. For example, prevent Romania from jumping to latin.
I believe in this era there's still the possibility of writing Albanian with the Greek alphabet, and the Russian Empire could Cyrillicise most or all of their Latin-using ethnic groups, except maybe the Poles. Possibly it could even be promoted as a nationalistic measure if it's early enough and they play the right cards, at least for Finland and Estonia, as the earliest Finnic-language texts (an old birch-bark letter) are written in Cyrillic.
You definitely need a waaay earlier POD for this to happen with organically occurring scripts.
Maybe, just maybe, you can get some conlang script to take off. There were many phonetic alphabets created in the 18-19th centuries, mostly by philologists.
This, combined with creative nationalism. By that, I mean having Hungarian readopt the rovas runes, which perhaps could spread to Finnish and Estonian. Glagolitic could be used for various Slavic languages in this case, basically whatever isn't Russian in some sort of nationalistic backlash. Or even better, an artificial Slavic script, since I know there's some pseudoscience/pseudoarchaelogy floating around about pre-Christian Slavic scripts which seems easy to create for anyone who wants to invent a tradition. Germanic countries could revert to Germanic runes.
This would probably be in some sort of fascist Europe following certain strains of fascism which would reject the recent Christian past in favour of pre-Christian local traditions (be it the Romans/Greeks or some glorious pagan past). It could flow to the colonised world from there, either by rejection of their own Abrahamic (antisemitism is inevitable here) traditions--Islam in this case--or just encouraging locals to create their own scripts (perhaps in preparation for independence, since these fascists might tend more toward internal splendor rather than imperialism of "lesser races"). There's quite a few indigenously created African scripts to write African languages after all. Same with Asia--for instance, the Indonesian fascists could use Javanese or some other pre-Islamic script for their language and others.