I had a clump of black locusts cut down a few years ago. If you know anything about black locust, you know that when you cut one down you'll have 1000 more next year until you chemically kill the roots. This stuff was recommended by a tree service (not the ones that did my trees mind you) and it worked first time. The secret is in how (and when) you apply it.
https://www.tractorsupply.com/tsc/product/brushtox-brush-killer-wtriclopyr?cm_vc=-10005
You have to cut around the stump to expose fresh tissue in the phloem layer (the layer between the bark and heartwood) as this is what will transport the chemical to the roots. Doesn't have to be deep, just enough to expose it. All I did was take an inch off the top of the stump. Then paint the Brushtox on immediately after exposing the fresh layer and let it dry. Reapply in 20 minutes. Be generous with it. But you have to do this in the fall when plants are naturally sending sugar TO the roots instead of OUT of the roots. If you do it in the spring, it's just going to get pushed out so wait at least until August to do this if you decide to go this route.