SFPL does give cards to children. Only those under 12 years of age need have a guardian's permission.
I wish you luck with the project. I'm not sure many publishers would agree to have books freely distributed in this manner, given recent stories like the "massive wave of e-book piracy" one.
You might look into "Educational Fair Use" copyright policies. Most universities insist that materials falling under that provision be assigned directly by a teacher, but it's still a good starting point.