Writing on his blog, John Goodman says that refundable tax credits for other insurance policies are preferable to SCHIP. (For the sake of the blog post he concedes the point of a societal interest in funding health insurance).
A $1,000 refundable tax credit (meaning it goes even to people who don't pay any taxes) would come out of the current budget for SCHIP, as well as DSH payments (taxpayer money that goes directly to hospitals for treatment of people without insurance).
Goodman cites 4 reasons why this idea is preferable to expanding SCHIP.