Ammate salt crystals are sometimes available in feed or garden shops. Any salt or acid will speed the rotting process. Drilll holes in the stump and add the salt or acid. Be careful, when handling acids. Be sure to use rubber gloves.
Mother nature can be of great assistance.
You can cover the stump with rich top soil. The bacteria in the soil will help break down the wood. It will also draw beetles, which love to eat wood in dirt. This may occur under the black plastic, as well. Many tree companies have stump removers that saw below the soil line.