Well, for a post-Islamic conquest Byzantium, they had about 5 years to do this conquest before the Sassanid Empire stopped existing. I'd say that without a conquest in preislamic times (rolled back, of course) there'd be no way to have a conquest during Islam.
Assuming that the Byzantine Empire had somehow conquered Mesopotamia and Iran and held it for some time, you'd need another great Byzantine general like Belisarius or Narses, to head east either around 700 or 750. He'd destroy the Umayyad caiphate at Damascus in either event, then march down Mesopotamia. Once Mesopotamia was in Byzantine hands (much like the campaigns of the late 500s/early 600s), the scattered, divided Islamic factions could be defeated, with many probably reconverting, especially from the 'Umayyad side. Then it'd be another huge campaign to get into Iran, but the Muslim presence there wasn't as strong as it was in Syria/Iraq/Egypt, and if this all happened around 700 there wouldn't be much establishment out there anyhow.
For a preislamic conquest, once again look at the 500s-600s. Have the capture of Ctesiphon come earlier and with less trouble, then have a civil war divide the remainder of Persia so the Romans could lick their wounds and keep marching on. They couldn't hold Iran, but they damn well could conquer it.