I recall seeing a product at home depot where you drilled holes in the stump,poured the product into the holes then lit the product. It would burn into the roots killing the stump. I don't know if it is still available. You could also contact a arborist from the yellow pages and ask how they kill a stump.
We cut a tree down next to our house. To kill the stump I cut it back as far as I could, next to the ground. Then I covered every bit of the stump up so it would not have any exposure to the sun. I used a metal bucket. You could probably use anything that would block out light and be sturdy. then I covered the bucket with dirt. The tree never grew anymore. It worked for me.
Each time you barbeque and use charcoal, or build a fire in the fireplace for the winter, put the leftover red hot coals onto the stump. Make sure to water the surrounding area to prevent fire. It will burn the stump out over time.
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