Can I claim preschool tuition for my granddaughter without claiming her as a dependent..?

You cannot claim any education expenses for her if she is not a dependent on your tax return.

Q. Can I claim preschool tuition for my granddaughter without claiming her as a dependent?

A. No.  But, the parents may be able to claim what you paid, depending on what tax benefit, you're asking about. 

The general rule is that a taxpayer must actually make the payment to get the deduction. However, there is a tax court ruling that seems to say that he/she can take the deduction even if you were they one that actually paid it under  the theory  that your paying the expense is just a gift to him, and it was therefore  really his money that paid it.