....and Byzantium never stops suppressing the Copts. (remember that Egypt was part of Byzantium until the Muslims liberated it)
Calling the Muslim conquest of Egypt a liberation is a bit of a stretch - it was really just a change of foreign rulers.
And even though Muslim rule was initially more tolerant than Byzantine rule had been during that period (IIRC the supression of Copts under Byzantine rule has never been as bad as during the period right before the Persian and Muslim conquests), the Copts would eventually face varying degrees of persecution under Muslim rule as well.
I know its probaly been done before but
Coptic Christianity remains number one faith in Egypt. Christian Egypt erupts as independent Christian Kingdom
What happens next will depend on how and when Coptic Egypt becomes independant.
There are several ways to let this happen, but IMO the best way to let this happen, will be to let Heraclius stay in Constantinople or attack the Persian armies in Anatolia, instead of going for the barely defended territories in Persian Mesopotamia.
Then let Heraclius succeed in defeating the Persians in Asia Minor, so that Byzantium retains Asia Minor and the Western Caucasus, but fails to regain most of Syria, the Holy Land, and Egypt.
With Egypt and Syria, and after a long war againes the Byzantines, the Sassanid Empire has quite overextended itself, and as Khusrau II wasn't a very good administrator, it isn't too hard to make the Sassanid Empire collapse at this point.
Just let Khusrau remain in charge for a few years longer, and then make sure that after his death, a succession struggle breaks out. (which shouldn't be too hard - Khusrau has imprisoned his eldest son Kavadh, and Khusrau had various other enemies as well)
This succession struggle then greatly undermines the strenght and stability of the Sassanid Empire, resulting in opportunistic raids from the Khazars, Western Turks, and Arabs (in order to prevent the Muslim conquest of Egypt in this scenario, the rise of Islam or at least the unification of Arabia by the Muslims should be prevented, though), which then weakens the Sassanid Empire even further.
And at that point, all you need is either a Persian general who moves into Egypt and declares himself independant, or a Coptic rebellion that results in the Persians losing what little authority they had left in Egypt, and the subsequent establishment of a Coptic state in Egypt.