IMHO, any animal in north america with the exception of possibly a big bruin can be instantly and reliably dispatched with a point blank shot with a projectile over 8 grains delivered at 1,000 fps or more to the brain (if known) or to the area immediately south of the skull to where the spine joins the brain stem. It is instant and all over humane dispatch.
I "brain" hogs with a high power .177 pellet rifle no matter the size of critter... They drop to their knees dead 100% of the time no matter their size...
If you look up the term "pithing" and translate it from blade to projectile, you will understand the brainstem/spine connection point and resulting humane death.