So many great suggestions. A question here--is there some teething going on? Sometimes biting is a great relief for their little mouths, and if there's a lot of drool, that's an indicator. Teething can also happen without any immediate breakthrough, as the teeth have quite a journey before eruption.
If your son needs to be sitting on your lap, when you provide the correction, ("Biting hurts." and offer a suitable substitute) be sure to turn him around facing away from you, so he can focus on the toy/teether. I would curb the furniture biting too. Can you offer a damp washcloth which lives in the freezer sometimes? The cold can offer relief. Some children like teethers, some don't. There's a company that makes strap covers, so when babies chew on the straps of a carrier, they won't destroy the fabric.
Be consistent with providing suitable alternatives, be sure to put him down when he's biting you as another poster suggested (or, as I mentioned, turn him away so there's no face-to-face contact---he'll eventually get the message) and keep up your great attitude--kids often don't bite with intent to hurt until they're quite a bit older; and then it often has more to do with a lack of social skills than any malicious intent. Your baby is very lucky to have such an understanding mom!