You guys are comparing apples and oranges.
A firing squad shot a criminal from approximately 25 or 30 paces, and even though they sought out the best marksmen, criminals were often wounded or completely missed, requiring a second or even third volley. With very few exceptions, electricution quickly dispatches a person. Thus, the determination that a firing squad was "cruel and unusual punishment".
I will go out on a limb and guess that dogs put down with a .22 are typically shot from only a few inches away, making it a foregone conclusion with no chance of missing. I cannot believe elecrocuting a dog, hanging an animal with neck muscles like a pit bull, or slamming a dog down repeatedly are quick, clean, or (by any definition) humane means of euthanizing and animal.