Certified GKH Gardening Expert
If you can't use chemicals, you will need to dig them up or continually mow them down when they start to appear. Either method will get rid of them eventually without chemicals.
Personally, if I were you, I would post on a local message board that you have free daisies to anyone who will come dig them up. Normally, you will have more than enough people volunteering to remove them for you so they can plant them in their home.