Depending on how old you or the child is, you can always utilize the cash value amount in a whole life insurance policy. If you have one in place with the amount needed to pay for college, you can take a loan against the policy without having to pay it back and still keep the policy at the same time.
Federal loans (such as the Stafford loan) are not based on your credit history. You will not need a co-signer, or good credit. With private loans there is no way around needing a good credit history. If you're in foster care, talk to the people. There is a program which provides tuition, room and board money to children who were in foster care until they went to college. The problem with Federal Government loans like Stafford are that the student with no credit history can not fully fund their tuition with a Stafford loan. Stafford has very low limits (like 2,650.00 in freshman year).
It is impossible to get a student loan without a co-signer even if the co-signer makes over $19,000 as another person as suggested. I was the victim of a scam and my credit got ruined. My Dad has excellent credit but no one will approve a student loan with him as a co-signer because he's only been at his current job for 6 months. My fiance has ok credit and makes almost $40,000 and they wouldn't accept him as a co-signer either. I have applied to every bank and loan company I could find on the internet. I even started calling to find out their minimum credit scores to see if it would even be worth while to apply. I got the same answer each time "we don't give out that information". They all just wanted me to apply and "see" if I will get approved. I told them I know they wouldn't approve me because I've applied to all of them before.