Ideally, before grinding the stump you could have drilled it full of holes and poured Epson salt in them to kill the stump. Now that the stump is gone, you don't really have a centralized target to attack so you're stuck with their gorilla warfare attacks.
As others have said, you can just mow them off. Trees store energy in their roots and that energy is available to sprout new growth when the tree gets cut down. As soon as the root system has exhausted all of its energy trying to sprout new growth, the root system should die and the problem should go away. Try to keep it from growing leaves as they start storing more energy in the root system right away.
If you're going to use a herbicide, you might try something with triclopyr in it. If you get some that's ag strength, you can cut it 50% with diesel fuel and apply it to the cut stems. You might be able to thin it down further and spray it on the foliage. It's a broadleaf herbicide. When applied in the correct concentration, it will not kill your grass, but will kill dandelions, creeping charlie, and will knock the crap out of clover. In concentrated form, it can be painted on the sides of trees, vines, and ivies to kill them. Personally, I'd just use the lawnmower.