This tenacious weed is quite noxious and not the easiest to control. It has a deep extensive root system that tolerates the poorest of soils. Using a non-selective weed killer such as glyphosate (tm Roundup) would be a good option but would need repeated applications when the plant is in flower. However you indicate you would like alternatives. Unfortunately they are not attractive ones. One way is continue to pull up the shoots. However, this may take up to 3 years for the roots to finally be starved out, as any roots left in the soil will regenerate within 2 weeks. Another option is smother them out by excluding sunlight. So something like black plastic of landscape fabric can be placed on the area, being sure to cover all the edges so any bit of light is excluded. Again, this is a multi-year battle. Sorry there isn't a better solution.
