Good old fashioned vinegar does the trick for me - the strong stuff(10%)sprayed directly on plants kills them off for quite awhile.

I, too, use white vinegar as a weed killer in certain areas, such as between bricks. I only use vinegar where I have no intention of planting anything. For instance, I have some tough native grass growing in my gravel driveway. I used full-strength vinegar last year. It killed the unwanted grass, and kept the grass from growing back for six months.
Lorna

One solution that might work is boiling water staight off the stove. Mind you it is tedious and you have to do it a few times before it is 100% successful. It you have a small area it works great, larger areas I use my husbands blow torch first on the leaves before I use the boiling water.
Sharon

Vinegar is amazing. Thanks! I'll try it this spring.

Here is a link to an all natural herbicide.

Here is a link that might be useful: All Natural Herbicide