As you've found out, trying to get rid of them by digging them out
isn't very effective, not to mention a pain to do. They can have
roots a couple of feet deep and unless you get most of it, they come
back. I'd go with spot treatment with a broadleaf weed killer, like
weed b gone. Use a small tank sprayer which will allow you to deliver
it right to the target, meaning you will use very little herbicide.
Once you get rid of them, in a thick healthy lawn, you should only have
a small amount in the future, which you can deal with the same way.