13-year-olds aren't legally allowed to work in the U.S., but that doesn't mean he/she has to wait until age 15 to learn the value of a dollar! Ask neighbors if they need their lawns mowed, weeds pulled, or pets looked after while they're away. There are tons of ways your child can make a little extra cash and also practice maturity, responsibility, and working for another person. Just ask around to your neighbors or friends to see if any of them would be willing to "hire" your child, or put him/her to work yourself by establishing a pay scale for certain chores done around the house.
You can probably find some close friends or some neighbors who have young children, they could babysit. If some neighbors or friends have dogs they could walk dogs. I think dutchwonderland, in Lancaster Pennsylvannia would hire anyone 13+. Thats all I know of!