Coalition warfare is one of the Strategist's oldest problems
What your alt history world is facing is what sovereign states have faced since at least as long ago as Sumer and Babylon. A nation or a kingdom has to appeal to another nation or kingdom and convince them to risk their blood and treasure for {a reason}. A great model for you to use to apply this coalition warfare problem to your scenario is the period from 1789 to 1815 in Europe. Why?
It was the period of coalition warfare (against Revolutionary France) - it took Six Coalitions to finally defeat Bonaparte, and between times the alliances shifted and moved as the motives and goals of each crowned head in Europe changed.
We used that period at Staff College to consider core problems in coalition warfare. (We also examined The Peloponnesian War and WW II). What makes the Napoleonic / Revolutionary period a great model for you is that there was a profound cultural motivation to oppose Revolutionary France: the French Republic's goal was in direct opposition to the cultural baseline of the ancien regime in that it sought a fundamental change in how society is structured - (1) no more family owned kingdoms and (2) a reduced role of the church in the social structure, or even its removal from it.
Let's apply that tension to your Byzantine versus African analogues in your fictional world.
Step 1: establish what about this Byzantine-style Empire is profoundly different from the culture of the ten kingdoms / empires who oppose it
Let's pick a couple of easy ones: religion and language.
Monotheism (of a sort) Byzantine practices versus polytheism and / or animism (of a sort), and even a collection of all of them among the ten kingdoms.
Language:
All of the African-analogue nations have something like a Romance Language relationship to one another's languages. They have established a lingua franca and are able to easily communicate with each other, regardless of how much they dislike each other. The Byzantines, on the other hand, speak some barbaric tongue with an indecipherable script / alphabet ...
Step 2: Despite their differences, all of the kingdoms agree that they don't want that (language, religion, both) jammed down their throats.
Result? They form an alliance against that, and when it's over they are either better friends than before or they fall into bickering again.
You can come up with a few more cultural taboos - those Byzantines practice human sacrifice! - which the African empires and kingdoms not only don't accept, but won't accept, to justify why they ally against this foreign threat.
All they need to be is good friends until the war is over: see the US and USSR versus Third Reich for a fine example of that. Afterwards, they can go back to their standard antipathy for one another.