I've experimented with different forms of intercession when praying with children, and I've found the following to be very effective (with instructions beforehand that children can pray out loud or in their hearts). The children don't often say prayers out loud, but they get very intent and quiet and focused.
It introduces the different types of prayer, as well as broadly following the structure of the intercessions that happen in church.
You can add "Lord in your mercy / Hear our prayer" or "Lord, hear us / Lord., graciously hear us" between each petition if you like.
If there's anything you want to say thank you for, you can bring it to God.
If there's anything you want to say sorry for, you can bring it to God.
If there's anything that's making you scared, or worried, or sad, you can bring it to God.
If there's anything you want to ask God's help for, you can bring it to God.
If there's anybody you know who is ill, or having a problem, you can remember their name before God, knowing that he will give them strength and help.
And if there's anybody you know - a grandparent, a parent, a friend, a pet, or anyone else - who has died, you can remember their name before God, knowing that he has given them new life in his kingdom, where they will live forever, where there is no sadness or pain or death, and where God himself will wipe away all tears from our eyes.
Merciful Father, accept these prayers for the sake of your son, our saviour Jesus Christ.