| Ultimately the responsibility of raising/training the children falls on the parents. It is the parent's responsibility to "Train up a child in the way he should go".
Here are just some of the scriptures that make reference to this:
Deuteronomy 6:7, Proverbs 22:6, Proverbs 22:6, 2 Timothy 3:14-15
Here are some scripture references from "The Message"version which I think
explains them well:
Deuteronomy 11:18-19 "Place these words on your hearts. Get them deep inside you. Tie them on your hands and foreheads as a reminder. Teach them to your children. Talk about them wherever you are, sitting at home or walking in the street; talk about them from the time you get up in the morning until you fall into bed at night. Inscribe them on the doorposts and gates of your cities so that you'll live a long time, and your children with you, on the soil that GOD promised to give your ancestors for as long as there is a sky over the Earth."
Deuteronomy 4:9 "Just make sure you stay alert. Keep close watch over yourselves. Don't forget anything of what you've seen. Don't let your heart wander off. Stay vigilant as long as you live. Teach what you've seen and heard to your children and grandchildren."
Ephesians 6:4 "Fathers, don't exasperate your children by coming down hard on them. Take them by the hand and lead them in the way of the Master."
Psalms 127:3-5 "Don't you see that children are God's best gift? The fruit of the womb his generous legacy? Like a warrior's fistful of arrows are the children of a vigorous youth. Oh, how blessed are you parents, with your quivers full of children! Your enemies don't stand a chance against you; you'll sweep them right off your doorstep."
1 Peter 2:9 "But you are the ones chosen by God, chosen for the high calling of priestly work, chosen to be a holy people, God's instruments to do his work and speak out for him, to tell others of the night-and-day difference he made for you—from nothing to something, from rejected to accepted." This counts for you parents as well :-) Teach your kids this stuff! You'll be glad you did!
I mention these scriptures here because raising up a child in the Lord cannot and does not happen on Sunday alone. It must be happening throughout the week at home with the family.
I have created a list of family resources that will help parents pastor their own children. Many of these resources helped my wife and me with our own children. Check out the Family Resource page and start spending time with your children learning about God and all He has for your family. I will also be working on a Bible study page that you can use with your family as well. These will be the Bible studies I have been using with the children in the older classes.