There are many stump killing products available to homeowners. The most common active ingredient in these products is either trichlopyr or glyphosate. Read the labels of these products carefully before purchasing to ensure it is labeled for cut stump application. Once you decide on a product, buy the smallest container that will get your particular job done. Any product stored on the shelf of your garage or shed is a potential hazard and has a finite shelf life.
Well, clearly the best way is to keep hacking and dig up. I appreciate that this can be a big ask depending on the size of the tree. You can try scoring the top a bit like this ###. You can go for a shrub type replacment for your tree, willow looks great. If you must use chemicals the answer above will do. You can also try boring a small hole and pouring a small amount of deisel in every week for a few months, that should kill it.
Cy Marven