I believe that the power of the word of God will work for kids as well as adults. Paul says in 2 Timothy 3:15-17 that what Timothy had learned from the Word was from what he learned as a child. Here is what those verses say:
And that from childhood you have known the Holy Scriptures, which are able to make you wise for salvation through faith in Christ Jesus. All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work.
We as adults need to encourage children to trust in God's word. While the word is for teaching, corection, etc. it doesn't get done on its own. To work on kids, it has to be taught to them. We adults must build faith in our kids. We should tell them about a God who will come through for them and encourage them to trust him because he is faithful.
We need to tell what's important about the scriptures. Its good that a kids knows David had 5 stones and a sling shot and that Jonah was in a whale 3 days and nights, but the point of those stories is victory over giants in life and trusting and obeying God. They should have learned to walk in the power of God’s covenant and to believe God is in covenant with them just like He is with adults.
The lion's are not what are important in the story of David. Its the point that Daniel stood up for what he believed in - God - and wouldn't trust in anything else no matter what happened to him. He recieved supernatural protections from the Lord and learned to trust in Him. The story could have been about rattlesnakes or even bears.
Children need to know about the principles of God's word so they can put them into practice. If all they know about the word is "cute bible stories" then all they will have is that. If they know how to use God's word and the principles for living behind those cute stories then they will be victorious in their lives at a young age.
If all we ask kids to do is "sit down and be quiet" at church, then that's what they will grow up and do. We already have enough adults just sitting around and doing nothing in church. We need kids who are on fire for the Lord and know His word and that it applies to them.
Please don't forget that "Faith comes by hearing and hearing by the Word of God" (Romans 10:17). You must teach them the Word. If not, then they can't have faith without knowing what the Word says. Don't just teach Bible stories: teach principles for living.
Whatever your role is: working in kids ministry, parents, grandparents, etc., please remember to teach the Word and how kids can apply it to their lives. Make sure the kids you have contact with are prepared for victorious living through God's Word.