The earliest extant manuscript to favour ἀπιστίαν include C (Ephraemie Rescriptus; 5th C.) and D (Bezae; 5th C.). C is considered a weak Byzantine text in Matthew's gospel1.
Textual critics tend to favour ὀλιγοπιστίαν over ἀπιστίαν for two reasons:
ὀλιγοπιστίαν is the harder reading2. See for example Metzger who says:
It is more likely that the evangelist used ὀλιγοπιστίαν, a rare word that occurs nowhere else in the New Testament (though ὀλιγόπιστος is used four times in Matthew), and that, in view of ἄπιστος in ver. 17, copyists substituted the more frequently used word ἀπιστία (which occurs eleven times in the New Testament), than that the reverse process took place.3
Comfort agrees with this assessment, saying that ἀπιστίαν 'is a scribal substitution, carried over from 17:17. 4
This is a theological reason, best summarised by Comfort.
"...there is a difference between the faithless generation of Jews who rejected Jesus as the Messiah and the disciples who had faith but not enough, in this case, to cast out the demons."5
The general consensus of opinion seems to favour ὀλιγοπιστίαν (little faith).
1 See Text-type in Codex Ephraemi Rescriptus.
2 also known as Lectio difficilior potior (Latin for "the more difficult reading is the stronger") This is the principle of textual criticism that states that where different manuscripts differ the more unusual word/ phrase is more likely the original. The understaning is that scribes would more often replace odd words and hard sayings with more familiar and less controversial ones, than vice versa.
3 Metzger, B. M., United Bible Societies. (1994). A textual commentary on the Greek New Testament, second edition a companion volume to the United Bible Societies’ Greek New Testament (4th rev. ed.) (p. 35). London; New York: United Bible Societies.
4 Comfort, P. W., Tyndale 2008, p51.
5 Comfort, P. W., Tyndale 2008, p51.