Drill several 1-inch deep holes in the top and side of the stump. The number depends on the size of the stump, but start by drilling them 3 or 4 inches apart. Drill the side holes so that they angle downward and won't let fluids spill out.
Fill each hole with about 5 ounces of saltpeter and top off each hole with water. Let the stump absorb the chemical for 4 to 6 weeks. You will notice the stump soften with time.
Come back after 4 to 6 weeks and fill each hole with kerosene. Wait another 4 to 6 weeks for the stump to absorb the fluid.
Set several burning charcoal briquettes on the stump and wait for them to burn all the way through the roots. This may take several days, and some attention should be paid to the charcoal. If it looks like the fire is slowing, add more charcoal.