I have tried everything under the sun and nothing kills these sprouts. I'm about to pull my hair out one strand at a time.

Anyone have any insight?

Roundup Brush killer will do the trick but it also kills the lawn where you spray, it pretty much kills everything.

Roundup Brush Killer is only a temporary fix. I get these every year, but nothing does the trick permanently. I appreciate your comments

Even digging out by hand or using a year long extended killer will not prevent the annual dropping of seeds. Short of cutting down the tree there isn't much that can be done to prevent this from happening. Sorry, didn't know you wanted a permanent fix, this looks like a yearly maintenance issue.

I'm a bit late to the party...

I have the same issue. Cut down 2 70' black locust trees and now my back yard looks like a jungle after 2 weeks. The stumps were grinded but the roots remain. Beginning in the late spring (northeastern us) the sprouts began in little spots. I sprayed with weed killer, waited a week and mowed. So far so good but others continue to sprout.

Based on previous comments, I'm going to assume these will grow back next year where I sprayed.

Best solution, remove the roots... ta-dah. But that's quite a bit of digging and cutting. Mow down for a few years and the roots will decay, good sign of decay is mushrooms in your yard like mine.