How can I get my new cat to stop biting?

My husband and I adopted a second cat from our local Humane Society. He gets along great with our other cat, and he's a good cat for the most part. He loves to snuggle and is a purring machine, but he always bites when being cuddled. He doesn't try to leave at all, and he's happy and purring, but he'll just spontaneously turn his head and bite our arm when we're petting him. He's not sore at all, as I had him checked out by a vet. He just has a bad biting habit. We've tried spraying him with water when he bites, and he's completely unfazed by it. We've tried saying 'NO' sternly, and he doesn't stop. We've tried everything we can think of, but he won't stop biting. Does anyone have any (humane) suggestions? I want to be able to cuddle him without being constantly bit.