Very difficult as the roots of the tree obviously are spread under the grass. If you apply something particularly noxious it may damage the main tree and although that's unlikely I have seen it happen. A paint-on weedkiller will knock down the individual suckers but you'll always have more to contend with. How far away's the main tree? Consider drastic action, digging down and severing the roots which travel your way and putting down something to block their further ingress?