Bullies themselves need counselling on managing their own needs and emotions rather than punishment. We focus so much on the victims, we also need to focus on the perpetrators and see them as victims as well if not of anything else than their own psychology.
Bullies often reflect the environment they're grown into: bad, absent, abusive or too demanding parents etc. They should be helped before resorting to punishment, but any attempt is deemed to fail if their family refuses to cooperate, which is the most likely case since it implies admitting they suck at parenting.
A prime example, the kids next door when I was growing up. They were younger than I was and never would try anything alone but two-on-one they would sometimes. (Usually when a third troublemaker was on the scene.) One time I was defending myself against an attack with a belt, I disarmed him and threw the belt into the vines growing on our house--high enough up that it would require a ladder to reach. When the belt was recovered the buckle was missing--they called the cops saying I must have stolen it. Just from talking to them the cop figured out I was acting in self defense, I had no possible way of having stolen the buckle (the instant I had control of the belt I threw it), the buckle must have come off when I threw it, bad luck for them. If the cop could figure that out so could their parents--yet they still felt I had stolen it since it couldn't be found. (Turns out there must have been a crack-the-whip effect, the buckle came off and flew completely over our house. We found it in a flower pot on the other side of the house two years later.)