We have a helpful group of parents in our troop that started with good communication and peer pressure. Our group of 14 girls are very active and inquisitive they are hungry to become better scouts. It starts with an agreement with the parents that you'll run the troop but parental support isn't an option its expected in one form or another! Parents can help by donating money, craft items, or time. Hold a parent meeting either in person (best) or via a phone meeting and have a sign up sheet where you ask up front for help for the variety of events you are planning.
It's really a good idea to plan your troop's regular events in advance. We have a meeting plan for the whole school year which is subject to change but lays out the badges we'll be working on and what assistance is requested. It is sent to all the parents via email and everyone is asked to sign up and hit reply all. Everyone can see who volunteered for what.
Another great way to have parental involvement is have the girls thank the parents every time they help. Clap, and say loudly "Thank you Mr/Mrs X!!!" or 2-4-6-8 who do we appreciated Mr/Mrs X!!! write thank you notes, make a fuss because they did something wonderful, they gave their time and/or donated items or money to help the troop have a wonderful experience and pretty soon it becomes a habit to help and by the next year the problem takes care of itself. Have a wonderful year!