From the ArcaMax Publishing, Gardening Newsletter:
http://www.arcamax.com/news/gardening/s-1893-563111
Question: My wife is very sensitive to poison ivy, but also does not
want to use an herbicide. Is there any sort of shrub or ground cover
which would choke out the poison ivy? Do you have any suggestions for
eradicating it?
Answer: Unfortunately, there is no plant that can outcompete the
poison ivy. You might be able to smother at least some of it by
cutting it off at ground level or digging out what you can, then
covering the root area with heavy cardboard or numerous sheets of
newspaper, then topping that off with a heavy layer of organic mulch.
If it manages to come up through that, cut it off again, then replace
the covering. Eventually the root reserves should become exhausted.
There are some new, soap-based herbicides that are considered quite
environmentally friendly and safe to use. Avoid using a flame weeder,
however, since the smoke from burning poison ivy can be extremely
irritating to lungs.