What does your contract say? Are they paying for the day or do they have set hours in the contract? I would think your best bet is to make an amendment to the contract stating their acceptable arrival and departure times. I can see their side, you are supposed to be available for care the hours you specified in their contract they pay for a full day but if they opt to come late so be it.

It sucks to the provider, especially if you don't have other children in care while waiting for them. The only way to officially change it is to put it in writing and have both sides agree to it.