Certified GKH Gardening Expert
With these weeds, persistence and diligence are the keys. You have 2 options. The first is to keep a close eye on the beds and snip the weeds off at ground level as soon as you see them appear. These repeated attempts to regrow will eventually result in the plant using all of its energy reserves in int roots and dying.
The other thing you can do is use weed barriers. Layers of newspaper, landscaping cloth and even thick layers of mulch can act as barriers. This will prevent the weeds from getting light and they will die from a lack of sunlight.