According to Richard Bulliet in his Conversion to Islam in the Medieval Period, Iran was unusually early in attaining a Muslim-majority. Muslims reached 50% of the population in about 816 CE in Iran, about 166 years after Muslim armies first crossed the Oxus. Compare this to Egypt and Tunisia, where Bulliet puts this date at 864 CE. In Iraq it is also 864 CE , and in Syria it is about 888 CE. (I hope I'm reading these graphs correctly.)
From what I remember, the quantitative methodology Bulliet used to come to his conclusions was as follows. He made use of Arabic biographical dictionaries in which one can find entries on thousands and thousands of individuals. The topics of these biographical dictionaries are often very specific to place, for example, "the notables of [the Iranian city of] Nishapur." The entries are generally short and contain information on the genealogy of the subject. Using these dictionaries and the genealogies within, Bulliet made conclusions about the ancestors of these individuals who first converted to Islam.^1
Of course, there are many legitimate criticisms of Bulliet's methodology. If you read about the demographics of religious conversion, the author will usually tell you that it is very difficult to make any statement about the nature and numbers of conversion with certainty.
