You can girdle the tree, that is, cut away the bark _and the brown stuff
around the tree, about six inches worth, and it will die
in a year or two.
Black Locust can heal, so monitor and cut it away again if necessary.
Some people suggest girdling in two places to discourage it. If it
puts out leaves next spring, it's time to girdle again.
A spoke shaver is handy for the purpose.
Black locust also will send up shoots all over the place for a while.
Wildlife likes the dead tree, by the way.
Click to see the full signature.