Hi, Here's a related article I found online that could offer some insights for you:

http://www.howtodothings.com/education/a4098-how-to-get-grants-for-a-private-school.html

There's also an article on Education.com (from the National Association of Independent Schools) that you might review...

Financing a Private School Education
http://www.education.com/reference/article/Ref_Financing_Private/

It's one of the many articles in the Private School info center:
http://www.education.com/topic/private-school-options/

Here's info center on the topic of Gifted Children:
http://www.education.com/topic/gifted-talented-children/

Also: ask the school you are considering what scholarships or financial aid they offer for students.

Good luck!