Don't know if you can do burns of not, but we always put oil on the cut tree area after it dried out and let the oil soak in for a day or so then lite and let burn. Not only does it burn the trunk but down the roots as well so you may need to fill in the whole it leaves. We lived in the country and had many tree trunks to take out, worked fine and dandy for us.
A little more labor, but you can rent a stump grinder
Louisiana State has a good run-down of the various options when it comes to stump removal: