Everyone was so sure that Sirius was guilty, he was locked up in Azkaban... Lupin was alone in thinking he was innocent, and after some time, perceiving Sirius as guilty probably came more easily, made more sense. With James dead, and supposedly Peter too, there seemed no other alternative than Sirius, right?

Besides, look at Black's family. They weren't exactly supportive of the Light side - despite knowing Sirius for years, Lupin could have seen this as a reason to doubt his friend too.

The fact, though, that he was merely suspicious yet not certain of Sirius' guilt, indicates that he didn't truly believe the accusations, just suspected them. He was being careful.