All West African religions would likely survive for many centuries, unless you have a powerful state enforcing orthodoxy and repressing "paganism" and "idolatry" (imagine a Christian version of the Fulani Jihads, call it the "Fulani Crusades" or something). I doubt Christianity would be any different than Islam in that regard. Even though most West African rulers were Muslims, they generally showed a lot of tolerance to their non-Muslim subjects. Even if "suppressed" to the degree traditional European faiths are IOTL, there'd be a huge variety of rural and local traditions that would be directly inherited from pre-Christian times.
Ethiopia having influence in West Africa seems ASB due to the vast distances across swamps, rainforests, and the desert. Although there were Saharan trade routes with one end at Cyrenaica and Egypt, so you could have other sorts of Christianity enter into the region, especially if some equivalent of the Kanem Empire still exists, as Kanem would have the most contact with Oriental Orthodox states in Egypt and Sudan. So maybe Kanem(-Bornu) and the Hausa would be Oriental Orthodox of some nature, while the Songhai, Mande groups, Wolof, and other people to the west of them would be (nominally) Catholic.
I do think a native West African Christianity could easily develop. The Sahara (TTL probably called a word derived from a Berber term from the same root as Tuareg "Tiniri" meaning desert) is a huge barrier, and you could easily have some sort of heresy develop there which blends a lot of indigenous beliefs and customs or importing Berber interpretations of Christianity and further altering them. The Church in Rome would call it heresy, but they aren't really in a position to do anything about it since projecting power across the Sahara is very challenging and very expensive.
I would see that happening. My guess would be the West African Christianity would branch off from the Oriental Christianity, but still be considered an orthodox form of it with maybe patriarchs and such. And my influence, I would also mean in terms of writing and alphabet since that is also one big thing.