I've read that boiling water will work, if not permanently then you can redo the process. You can google and get lots of info, it's safe and cheap. I am planning to use it this year as a green alternative to weed killers, and to save my back from pulling the grass out of the crack between the sidewalk and the rock border on my flower beds! Good luck!
My experience has led me to believe that the only way to rid your self of grass is to use a shovel. It's a little bit of hard work but, it works. (Tilling works as well but, generally speaking I don't reccomend that people till unless they have a very large area to do. And still, you can turn the area with a shovel in sections.)