This, or activated carbon in powder form, or bentonite clay.

I would heat it up first - fill it with boiling water and let it sit until too hot to handle. Dump it out, dry it thoroughly. Take a sealable container (tupperware, etc) big enough to hold the mug, and start with an inch or so of your choice of drawing material. Put the mug in, and pack the inside and around the outside of the mug until the container is full. Let it sit for a few days.