I think the Handmaid's Tale season one only really came on to Now TV once the second season was hitting Channel 4, so it could be likely that season two would only come to Now TV next year when season three arrives on Channel 4???
Unless their rights change, it seems that Now TV will only get the show a year after Channel 4.
Having just finished series 1 I'd like to know this too. There's not much to watch on Now TV at the best of times, so hopefully they'll get off their backsides and get series 2 up there pronto, especially as they had previously promised it would be out in September.