Unfortunately, no. You can deduct medical expenses for yourself, your spouse, and your dependents. Only.
Your payments would be considered a gift to the child, and a gift to a specific person is not deductible as a charitable contribution.
If you paid more than $14,000 as a gift to the child, then you may have to file a Gift Tax return,
Form 706, Gift Tax
http://apps.irs.gov/app/picklist/list/formsPublications.html?value=706&criteria=formNumber&submitSea...Turbotax does not support Form 706, so you have to do that by hand.
Usually, you do not actually have to pay a tax, what happens is that your lifetime exclusion for estate tax purposes is reduced.
