Maybe after Stewie went to a Day Care Brian may have decided since he has been downgraded enough why not act like a baby and suck one of Stewie's pacifiers while playing with his toys. It would not be long before he starts to like it. It is a good theory It definitely would explain why you do not see him in diapers in the other episodes.
That actually happened in Family guy. Maybe after Stewie went to a Day Care Brian may have decided