I don’t know about charcoal, but I’ve heard that kitty litter will do a great job of de-humidifying a space. You can also buy a product (not sure what it’s called, I think it’s made of silica, I’m sure you could ask at a hardware store) that’s designed for this sort of thing. It’s the same stuff that comes sealed in those little packets in various products.
A container of that crystal cat litter would make an excellent dessicant. Spread some out on a small jar lid or bowl to maximize surface area. Less likely to draw vermin than rice, too.