Have you tried (it might be too late now) advertising for just summer care? Get a couple school age children in for just July and August to help bring in some income while you look to fill the spots for Sept onwards?

As for the one child...you need to sell the idea to them. At no point in time mention how you have been trying and no one is interested etc. Just sell the idea. How does this benefit their child? More trips to the park, more picnics, bigger outings. Time in the kiddie pool etc. Just tell them how much you are looking forward to having one on one time with the child, how they can lead your activities etc etc.

That said, working for just one child is often more work (no playmates) and it is less pay.

Oh, you could also advertise to take children just short term while their caregiver is on vacation. Many caregivers take summer holidays and many families still need care so you can look to bring in a bit of money that way.

Get creative with your advertising, it won't bring in long term income but it can bring in some money and change it up for you and your daycare child this summer.