I learned something when my son lived here and used to make beer in the garage. The weeds that grew up in the cracks in the driveway near the garage disappeared, and stayed gone for months. I asked him what he did, and he said he just dumped boiling water there.
Now, this doesn't work when it's wet and cold outside, but during the warmer, dryer months, I just heat up my teakettle and pour the boiling water on the weeds in the patio and driveway. It takes a few trips back and forth, but they disappear and stay gone for quite a while -- with no poison.
Another tip is to spray a vinegar/water mix on them. Try about 80% water to 20% vinegar for older weeds, or you can go even stronger. Use a plastic spray bottle and make sure to get the leaves good and wet.
