Can you use ratios? Tell her that you have a family interested in your last spot. That if she intends for you to care for her child then she needs to sign a contract and give a deposit and pay the weekly fees. Give a deadline or you will sign the other family on.

Tell her if she opts not to sign the contract and pay she can no long (ever) drop the child off as it puts you over ratio and makes you a criminal with severe consequences (fines and jail time).

If you are not full and have plenty of room for her then this won't work.

You will have to tell her that you open your doors at X time if she intends for you to care for her child then she will need to pay and make it official.

I would find it difficult to call this person a friend though. She has clearly cross some lines and knows it as no one just drops their child off without first having discussed an agreement for care.