I got rid of about a dozen stumps a few years ago. I cut flipped a 55-gallon drum upside down, added a 5" galvanized vent stack, and made a hatch on top. Then I filled it from trash wood and let 'er rip. On a good burn overnight, I'd have a hole 18" deep in the ground where the stump used to be.
The trick with burning stumps is you have to get them HOT ALL THE WAY THROUGH, otherwise they'll just char on the outside and quit. Once you get it hot enough it'll keep on burning on its own.
A couple of stumps were too big to fit the drum over. I chainsawed some vertical slots to fit the drum into and did them in two or three steps. Also, large surface roots will burn if you remove as much dirt as you can first.