I concur with May - though we've never actually been there in May because DW is a school teacher. We have been there in April, June, July, and August (almost every year), so we've got it bracketed.
May is one of the lesser traveled months because school is in session, whale season is over, and people on the mainland are not looking for a respite from winter. So less crowded. Also the weather in Hawaii has started to move more into summer patterns, but if the trade winds fail it won't be as hot and humid as it is in July and August during Kona (non-trade wind) weather.
Late September might also be a good time, especially if you want to spend time on North Shore beaches. With school in session crowds are lesser than in July and August, and winter weather hasn't yet arrived (meaning that North Shore beaches should still be suitable for swimming and snorkeling).
But anytime you can go is enjoyable. As others have mentioned, make the decision based on air fare and accommodation availability.