This is really out of all of our territories. There are so many possibilities. I will tell you my experiences with kids depends on what level of understanding they are on.

I never ever try to use the phrase, "just think how they feel now that you have done that" when my nephews or neices would physically hit one another or even bite. At the time these incidents occurred, they did not have the capability to emphathize, so to think how someone else would feel made absolutely no sense to them.
I basically said it is wrong to hit or bite your sister/brother, go to your room and sit quietly for 1 hour. If they did not go, I would escort them and close the door. No yelling from me, even if they were screaming. I would close the door. Occasionally they would bang on the door and scream and I would just hold the door closed saying absolutely nothing until they wore down. Sometimes they would just go to sleep or sit quietly. When I came back in, I reminded them there will be no biting or hitting or else they would have another hour alone. If they then stated NO, or started screaming again, I would just close the door and they had another hour. It would work especially well if they heard the others having fun. I never ever got mad or raised my voice. I just made it seem like it was common operating procedure. After a few times of Uncle Patrick, we all got along quite well because it was very clear I would not get mad, or give in. The rules were clear and enforced immediately, so they knew exactly what behavior caused their predicament, and they did not even test me after a few times over and we had very good times after that. Which was, I hate to say, very different from what they would get away with if my sister or sister-in-law had them. Chaos and frayed nerves. My wife would decline the chore with cousins because she never even disciplined our daughter.

My daughter was/is always so mild mannered... it worried me for a while. And she never even threw a tantrum. She just did as I said. Looking at her the wrong way would get the point across. Kids are so different, and at such vastly varied points in understanding, you really have to be observant as to what they do and do not understand. And I have found if punishment is just matter of fact, with no yelling by adults, its almost like the rules just stand on their own.
So I would say punishment should be
1.immediate
2. non-negotiable
3. and enforced without any verbal argument from the adult, the explaining is already done and is clear.
A few kids in the neighborhood I refused to look after. None of the above worked. Especially as the kids got older... it became easier to tell who would and would not follow the simple rules.

As for my experience as a child, my dad brought out the skinny black leather belt and had a wonderfully discerning ear for fake crying. And he beat the crud out of me when I took advantage of my mom when I was young. At about 10 years of age, I was pacified, and really started to understand that I was upsetting my mom.