The olde timey way is to drill a few holes to create a circle with a diameter roughly 2/3 the diameter of the stump plus some more scattered inside the circle (not as many, or as deep, as to cause excessive perspiration) and then fill them with "coal earl" (OK, if you can't get that stuff kerosene will do). Let the stuff soak into the stump - as in a week or two. Keep topping up the fluid in the holes and allow the stuff to seep into the stump as much as possible.
When the holes are basically dry (no overt pool of liquid) light it off to create a smoldering fire. If you get big flames and smoke either it's too wet or you have a volcano erupting. In the first instance smother the fire with stuff as opposed to drowning it with water, and wait another week before relighting. In the second instance take pictures and then run.
Let your stump smolder until you have burned out as much of a hole as you want. Take a pickaxe (or other impliment of choice) to the burned-out portion to get rid of the charred portion.
NOTE: Your local fire department may strenuously object to your doing this, especially if there are laws regulating the times when open burning or unattended burning are prohibitted. How your homeowner's insurance underwriter and the company that issued your policy will feel about it are anybody's guess.
stay safe.