Kohlberg believed that moral development is learned and that moral reasoning depended on a person's development stage. Moral development, therefore, is a function of a person's cognitive development stage. When faced with a moral dilemma, a person will respond in a way that is consistent with his current moral development. In the Heinz story, a man stole some life-saving drugs for his dying wife. The pharmacy where the drugs were available was charging an exorbitant amount for the drugs, which was morally wrong. The dilemma presented -- was it morally right for Heinz to steal the drugs? Kohlberg was more concerned with the reasoning used to arrive at the decision, not the decision itself.
So, you have to come up with a moral dilemma for a child in middle childhood. This means a child that is older than 5 and younger than 11. You must also be familiar with the stage of moral development (usually stage 4 of psychological development) at that age when you decide upon your dilemma. That is, don't choose something that a child in middle childhood is unlikely to have to face.
Some things that a child might have to face at this age might be whether or not to report his friend to the school authorities if the friend is doing something harmful to himself or others. For example, has a 10 year old brought a gun to school? Of course, schools are teaching kids to immediately report this, but it poses a moral dilemma for a child who is not mature enough many times to understand that the harm that child could do to others or himself outweighs the loyalty of friendship. Or, it could have to do with drugs - what if a child knows that his friend is smoking pot?
Another scenario that might work might have to do with a parent's teaching a child never to lie. This is a biggie for this age. Are there some instances when a child might think it is morally OK to lie? Maybe the parent is trying to quit smoking. The child finds a hidden pack of cigarettes under the couch cushion. Should the child flush them down the toilet? Or, the parent is an alcoholic. The child finds a bottle of bourgon behind the couch. Should the child tell the non-alcoholic parent? Things like this.