Do you pay for after-school care at this school? If so, you can claim that. If your child is in preschool, you can claim the tuition (up to a point).
Otherwise, no, private school tuition is not tax-deductible for the same reasons the payments on your new Mercedes are not tax-deductible - it's considered a luxury since there are public schools your child could attend. (Even though let's face it, at least where I live nobody in their right mind would send their kid to a public school unless they had no other choice!)