Since one of the tests to claim the child and dependent care credit on your return is that you must pay child and dependent care expenses so you (and your spouse if filing jointly) can work or look for work (i.e. the Work-Related Expense Test). If the expense is not considered "work-related," you are not able to claim it on your return.
Per IRS Publication 503 Child and Dependent Care Expenses, page 7:
Camp. The cost of sending your child to an overnight camp isn't considered a work-related expense.
The cost of sending your child to a day camp may be a work-related expense, even if the camp specializes in a particular activity, such as computers or soccer.