8T,
I feel your pain! Grinding the stumps is by far the best thing to do. If that's not an option there's a liquid product from Dow by the name of Tordon RTU that does a great job of translocating down, killing/preventing sucker growth. The cut to the suckers should be fresh for the chemical to work best. Cut the suckers or stump, give a little squirt of the Tordon and let it work. Little bit goes long ways. Don't do it prior to a rain and don't let it splash/drift on anything you want to save. As a commercial pesticide applicator I get squeeze bottle of Tordon from a distributor but it's probably available from local nursery or Home Depot type store. Their version may have another name. Look for something with Tordon's active ingredients: Picloram (5%) and 2,4D (21%). Please wear rubber gloves. Good luck.
Grassman