A story is just a story. But a Bible story becomes a Bible lesson when you use it to teach.
Be sure to have a main truth to each lesson. Boil it down to a simple imperative such as, "Read your Bible everyday." Then relate this to them in three ways in three appropriate places in the lesson.
To their mind: Tell them what.
This may be a simple statement of the truth.
To their emotions: Tell them why.
This does not mean to play on their emotions, but in giving the reason, they will begin to see why they should do it and feel that they need to.
Note: This is presented in the context of the truth presented and followed through on with the next step.
To their will: Tell them how.
This will give them the fuel they need to be willing to do it. If they do not know how, they will not take that final step. This may come in the form of a specific challenge at the end of the lesson (Read your Bible everyday by having a quiet time....) and always involve trusting God to help them succeed in their obedience to Him.
Make sure that the main truth fits the story that is being made into your lesson and use another scripture verse or passage to reinforce it. The main truth is really the teaching for the saved child. The Gospel is what is relevant to the unbelieving child because until he comes to the decision to trust Christ, he is spiritually dead (I Corinthians 2:14) and unable to understand God's Word and obey Him.