This is how I killed a plum tree my wife wanted us to keep, but I thought was pathetic looking, and was half dead anyway:
Use a 3/4 inch spade bit at a downward angle, then pour in full strength round up. Add a little more a couple days later.
To prep: Find a branch that has fallen off the tree, or take a branch from a similar looking tree. Whittle the branch so it fits perfectly into a 2x4. Since you’ll be doing this at night, practice pouring the round up and inserting the cover branch in the dark. Some sort of commotion out front helps. A fully charge cordless drill and very sharp bit helps.