One of my college-aged daughters recently asked, "How do I use the Bible to pray for people?" or "How do I pray from the Bible?" Forgot how she phrased it.
I had a friend once who collected blessings, doxologies, and prayers from the Epistles and read them out loud for people she was praying for. She was in a non-denominational Bible-loving, Jesus-loving charismatic church.
There are lots of prayers in Psalms and in the books about David. There are prayers that Jesus prayed in the Gospels.
Searches like this might be interesting for older kids.
You can search for prayers, promises, names or descriptors for God, Jesus, the Holy Spirit. This is like a word search but a little different. You probably won't find them all going through a concordance. You have to actually read the scriptures!
Take a Bible character and imagine knowing that person. What kind of person were they? What clues can you gather from the stories in the scriptures. Be honest about this. It will be quite eye-opening for everyone when you really look at the people God used and the people God dealt with. Alot of them are people you would never want your teens to hang out with! Yet, God has given us their stories to learn from.
I'm sure you can come up with more. Or you come up with the first search and let the kids come up with the next one.
Another strategy would be to pick one topic (the attributes of God or prayers or promises or . . . ) and collect them over a half-year or a year as you read the different lessons each week. You should look ahead and make sure what they're looking for can be found in the particular stories that you're scheduled to explore.
Play with it and see where God takes you.