I firmly believe children who are being raised in the church also need to be taught to serve in the church. Kids learn by example but also by practice. Children watching their parents teach a class or usher during service will not understand their role in the church only by observing. Some churches offer many places for children to serve. Others don't give kids a place to serve at all. If your church doesn't have a place for kids to serve then I would encourage you to find a way to change that. If your church does have places for kids to serve then I think you should take every advantage of that.
I've been so disappointed recently to have many parents tell me their children won't serve in church because "they don't want to" or "it isn't a priority for them". Children are children. They need guidance from their parents to do the right thing (if this statement confuses you please see this post). My heart is so saddened by the thought that parents wouldn't encourage their kids to do service for the Lord during church. If it is lighting a candle or collecting tithes or counting, whatever the service is your child should be involved if they have the opportunity. This prepares them for serving in the church as adults. Especially if your child is resistant, I think you should have them do it. As adults do we only have to do the things we want to do? Do we only do the things that bring us pleasure? Of course not! Allowing your child to think life works that way is setting them up for failure.
Serve the with gladness: come before his presence with singing.
Do your children serve in church?