Where would one hit a child if not on the face? How strange.
Usually on the bottom. Anywhere else should be left between consenting adults and not for punishment purposes. The only other time it is acceptable to hit a child somewhere other than his or her bottom is forcefully knocking them or jerking them out of the way of an oncoming car. If the child is about to get run over, you don't worry where on the body you touch them. You usually jerk them on the arm or knock them out of the way with force. It's better for the child to scratch up their knee doing that than to get run over.