Parents become very supportive when they know what you are doing.
1. Videotape a some of your lessons, games, outings, etc. and show them to parents. For added fun, find someone who can edit them and make a small video collage of youth events. Works great for youth group publicity too!
2. Invite parents along for youth events as chapperones and sponsors. To avoid child embarrassment ask children if the mind their parents along for the event. If they do, have parents work with a different group of youth that does not include their sons and daughters.