There are two things that I think would make this successful:
First, you are going to want to look for clients within the circle of people you already know. Put the word out among your child's classmates, teammates, and friends of the family. you're most likely bet is to find another kid who already knows your son and is the same age and has some interests in common.
Second, to make this look as professional as possible, you should map out the summer as different themed camps. figure out what kinds of things you would like to do with the kids and create a schedule. Maybe one week the theme is dinosaurs and you do a tour of the natural history Museum and then go hunting for sharks teeth in Maryland. Maybe another week you do military history and include a walk along the mall (World War II Memorial, Vietnam Memorial, Lincoln Memorial) and a tour of Mount Vernon and the American history Museum, another week you could do aeronautics and do tours of both air and space Museum's and a day flying kites somewhere. This will allow you to look a little bit more professional, and will allow you to figure out how much to charge for each week so that the fees related to activities (such as metro fees to do museums or admissions for places like Mount Vernon) are included in the price for that week. It will also allow people to opt in or out of different weeks, since most people have at least some weeks of family and travel or vacation planned.