If you wish to use a chemical approach, herbicides containing glyphosate, such as Roundup, can be painted on freshly cut stumps or stems. This works best in fall. There are other herbicides that can be used in this way too, such as those containing triclopyr. This technique uses only a tiny amount of herbicide, is targeted precisely, and the material will biodegrade completely over time. These two herbicides are used by environmentally responsible organizations such as Nature Conservancy to control unwanted trees. Make sure to follow all the label directions. Details can be found at the link.

Physically removing the stump is a very good way to eliminate the problem, if you are able to do it, since the planting area is then free of roots and quickly available for replant.

Here is a link that might be useful: Nature Conservancy

Thank you so much for the advice. Now I have a direction to attack. That is a great site too.

The "organic" way to eliminate a tree stump is as follows:

First, cut the stump off at ground level. This may require digging down around the stump to get clearance for your saw.

Second, go to an established forest, where rotting wood has accumulated. NOT a tree farm.

Dig up a bucket full of forest loam, preferrably from under a rotting tree trunk.

This loam contains wood eating microbes, bacteria and fungi that live off dead wood.

Take an axe, and chop into the top of the stump a few dozen times. This exposes more surface area for the microbes.

Cover the stump with the forest loam. Water carefully, don't wash away the dirt.

Keep moist. After a year, the stump should have rotted away.

Even four inch thick tree limbs left touching the ground will be half-rotted in a year's time.

I cleared my fenceline a few years ago and left the wood lying there when I got tired of chopping.

A year later, I tried to pick up the 4 inch thick tree limb to drag it out of my way and it snapped like a dry twig.

Wow, that's amazing. I have to admit I would never have thought of that, but it does make sense. I admit it will be dificult to do it since there are plants nearby but I will definately give it a try. Thanks. :)

Is it true that if you put salt on a fresh cut tree stump that it will die? This message did help me. I live where there are animals and kids. Thank you