Stand the watermelon on end in a bowl, stem end up, and cut a 3 inch diameter plug out around the stem like a Jack-o'-lantern lid. Remove the plug, scoop out about 2 inches of flesh, and pour out any excess liquid. With a long skewer pierce the flesh inside to the bottom in all directions without penetrating the rind and pour out any excess liquid.
Pour equal amounts of peach schnapps and vodka into the watermelon gradually until it cannot absorb any more and replace the plug.
Refrigerate watermelon on its end, plug end up, for at least 15 hours and up to 2 days.