I have thought about working out a timeline where Persia turns to Christianity in the fifth century, which makes it politically stronger, in effect the Emperor of Persia is a puppet to the church. As Persia grows strong politically it does so militarily as well, forming a formidible and capable Army and Navy, the original target is Constantinople. However the Muslims still come to power in Arabia and launch an invasion against Persia. The Persians wont stand for it and send its armies into Arabia. Most of the Peninsula falls to Persia and is forced to convert. The Muslims are restricted to a small country consisting of the two major Holy Cities, Persia is battle exhausted and can in no way fight the Byzantines, though they can hold their own.
Perhaps if you write your timeline, you can have the Muslims defeated by the odd coupling of a Byzantine-Persian Alliance at Babylon or Baghdad. The Muslims look west to Africa, they are able to take the Sudan and much of Sub-sahara Africa but fall short in conquering northern Africa. Many native African communities are now united by a common religion (Islam) and a common tongue (Arabic) and form into semi-powerful nation states in their own right.
Problem is Egypt hated the Byzantines, perhaps sometime after the Great Schism you can have a rebellion in North Africa and the Middle East. The People of Palestine, Syria, Egypt, and Carthage rebel and are assisted by the Persians and the Catholics. Egypt becomes the most powerful nation state among these and forms a rather large Empire. Only Syria is reconquered by the Byzantines.