OK, I'll explain. I did think you could see what she said but I guess not. The OP said her husband, an avid hunter shot the rooster 4 times with a pellet gun and it ran off. Now you know as well as I a .22 caliber round and a shot from pellet gun are not the same in ballistic results. I would think a .22 would kill a rooster quit well. So you in the country and me in the country is still the same. Before anyone shoots anything with any caliber round, know what it will do before the fact. Is it lethal or not? Come on, you know better.
If shooting a dog with a paintball is animal cruelty, then shooting a rooster 4 times with a pellet gun and watching it run off is certainly.
The OP did say later that they had already used the pellet gun method on a couple of hens with quick results. Granted, pellet gun is not my first choice - I'd prefer to use it to scare off predators. But since the hens they dispatched with the pellet gun were sickly, it makes me wonder if there was a stamina difference between a sick hen and a robust rooster, and the OP just didn't realize that the roo would last longer than the hens? In any event, I think they've realized that the pellet gun doesn't work so well, given the experience they've had.
My preferred method for dispatching a bird is the axe and block method. Just get a length of baling twine or something similar and tie a loop around the bird's neck, not tight enough to choke it or hurt it, but enough that you can hold its head in place over a wood block. I like to talk to them for a minute and calm them down before the deed, then off with their head! Make sure that the axe is sharpened beforehand, since it makes for a nice, clean kill.
I'm also somewhat of a fan of the bleeding-out method (like cones) because the bird simply goes to sleep from a lack of oxygen. From there, it's easy to behead them and finish the deed.