The most effective way to deal with a stump is to grind it out mechanically. The stump is typically cut down as low to the ground as possible before being ground out.
Once ground the remaining small roots will die off leaving the area free to be re-planted. Sometimes it is necessary to apply a stump killing poison. This is mainly in broadleaf trees.
We use Eco-Plugs which are completely safe and administer a minute amount of poison in a sealed plug without damaging surrounding flora and fauna. This would typically be done 4-6 weeks prior to grinding to prevent any left over roots from re-growing. Our Predator Stump Grinder will remove any stump down to a depth of 300-450mm. It requires an access width of 825mm. We can however provide other solutions for smaller gardens. See our stump grinding machine in action here: