I found this on the GW's landscape design forum Removing a Tree Stump with HIgh-Nitrogen using ~ rot stump gardenweb ~ as my search terms.

Buddy......get a tiger torch (20 lb propane) from a freind and some sort of steele covering to harness the heat drill some holes in the stump as deep as you can dump it full of gas or diesel and set it on fire and let it burn down.

Get a big bag of charcoal and soak some in charcoal liter and put it on the stump, light it up. The hot coals will burn it out. You can add fire wood as needed to keep the hot coals up. You can also use an electric fan to blow on the hot coals to speed up the burn. If it a big stump you may have to remove some of the ash and start again. I burned many stomps out like this. Give it a try. Let us know what you used.

I don't think I'd get hot coals anywhere near a gas line.

To rot more quickly, the stump should stay moist as often as possible. Anything green (as being the opposite of brown, in terms of decomposition) that you can pile on and maintain contact with the stump will help accomplish that, and speed the decomposition process by providing the nitrogen necessary to compliment the stump's carbon. Cut grass, kitchen scraps, will help it decompose more quickly. In the fall, covering it with a pile of leaves will speed the decomposition over winter by retaining moisture.

If you have a drill, put holes in the stump to expose more surface area to decomposition organisms, moisture and oxygen. I hope you are thinking in terms of years, it will take that long to rot.

If the stump will support a pot, you can put a potted plant there that you water often, until the top surface of the stump gets too craggy and crumbly to hold it.

Here is a way to enjoy the view while it is being broken down:

Oh that looks nice, and rotting nicely! I usually let sweet potato vine climb on/around my stump. It won't hold a pot anymore, but used to.

Plug the stump full of mushroom spawn. Oyster mushrooms will eat it up and you'll get mushrooms to harvest.

I have heard that pouring fertilizer down into drilled holes will accelerate the rotting action considerably. Also, covering it with earth to keep the little bugs and microbes working helps a lot. Keep it moist with a mulch cover even. If it dries out, the wood becomes more like petrified and will last a long time. Every time you pass by, piss on it to remind it who's in charge. So drill hole in top of stump and fill with a high nitrogen fertilizer. This is an organic way to rot stumps and will take about six months to work.

I get out my Sawzall (get a blade specifically for cutting wood), cut all the above-ground material, clear it away, then begin digging the dirt from the roots and cutting them with the Sawzall. A spade will pop the stump out, once you sever the tap root. I then fill in the area with garden soil, plant grass seed and forget about it.

I've removed 4 stumps just this spring - it takes a bit of work, but worth it!