I think the key is in defining discipline. Never use corporal punishment on someone else's child, even if you would use it on your own. One might make an exception if they have permission from the child's parents, but I would strongly advise learning new ways to discipline if you ever end up watching the children of non-spanking parents. Really, the best answer I would give is that, if all else fails, promise to tell the child's parents how they misbehaved, and let them come up with a punishment.
I recall once when my brother and I were being watched by a neighbor, my brother started throwing a tantrum. I don't remember why. When the neighbor started yelling at him, loyal big sister that I was, I started yelling at her to leave him alone. Our mother was told of the incident, and we both had to write letters apologizing for our behavior and thanking the neighbor for looking after us.
As I remember the incident, I admit I am still inclined to side with my childish self. Although I remember my brother could throw some epic tantrums, I also recall that this woman's children by her own admission were usually worse, and I remember plenty of times she sided with me over her own daughter. I expect my brother had simply had enough of her son and reached the breaking point.