For those who aren't badly allergic, begin with the following supplies:
1 sharp pair of pruning sheers
1 pair of good rubber gloves (they must be fairly thick)
1 empty 3-pound coffee can (do not use plastic)
1 paintbrush
1 pint of diesel fuel
1 pint of commercial vegetation killer (2-4-D or a product containing 2-4-D is preferable, but is becoming much harder to find in most places)
Carefully mix the vegetation killer with the diesel in the coffee can. Vegetation killer is toxic, and diesel is a solvent, so take care to avoid splashes or contact with the skin.
Immediately clip the poison sumac or other plants you are trying to kill, to within a couple inches of the ground. Dip the brush in the poison mixture and liberally brush the fluid on the fresh cut, coating the cut completely.
The gloves, can, brush, and mixture should be discarded after treating the poison sumac.
What happens is this: The diesel, which again is a solvent, acts to suspend the poison. It functions to deliver the poison to the deepest roots by reverse capillary action. In other words, it soaks in through the cut in the plant and is drawn into the roots. The diesel isn't the killing agent, the herbicide is, but the diesel allows the poison to reach all the roots. This would not be possible with normal surface treatment.
Within a week or two, the sumac will be dead.
Remember though that seeds in the ground will still germinate and grow into more sumac plants, which is why the procedure should be repeated. The branches and limbs that are trimmed should also not be burned as the smoke can carry the poisons in the sumac and can cause allergic reactions in the people who breathe the smoke. Instead, bury them where they can decompose naturally.
Using this method will remove poison sumac and other hard to kill but unwanted plants, while causing minimal damage to other plants in the vicinity. Care must be taken when using this method, however if you want to get rid of poison sumac and don't want to spend hours of fruitless and back breaking digging to do it, this will get the job done.