I would do one of two options depending on how fed up I was:
1. Provide an ultimatum. They either provide the necessary items to keep their child safe AND comfortable (I list exactly what I expect in my contract, and what I will provide), or they are breaching contract, and you no longer offer care.
2. Your purchase the items yourself as needed, and add EVERY. SINGLE. ITEM. to their bill. Trust me - I've done this. Rain boots. Coat. Sunscreen. Hats. Spare clothes. Diapers. It adds up. Sometimes in the hundreds for a month of gear. They will accept it the first few times, and then usually not return it (why would they if they don't bring their own items?), and so you keep repurchasing. I don't mean a separate trip every item - I keep a stockpile knowing it is inevitable. When they realize how much money they are wasting by not sending the child's own items - they will send them. I also charge $2.50 per item as a 'hassle fee' for myself.