@Laura2592 I just imagine this couple on the date that they need the babysitter for:
"Garçon! We are excited to be in your Japanese sushi restaurant. Please note that we will need twelve tacos, two Margaritas, and a gram of cocaine, and we appreciate you arranging that."
Jokes aside, I have no idea what the childcare options are like in the US these days, and if this is even a thing, but the only option I would feel comfortable recommending in this situation is a licensed childcare facility that allows drop-offs from one-time customers. It's hard enough to find something like this for pets, so I'd be very surprised if it existed in your area. But I wouldn't be shy about explaining why I couldn't allow a babysitter onto the property as an extra guest nor recommend a neighbor for in-home care. I wouldn't touch the liability implications and child safety worries with a ten-foot p(ed)o(phi)le.
If it's still an unconfirmed booking, I'd decline based on the guests' presumptuous tone - never a good sign. But if all else was looking fine aside from the babysitter issue, I'd be open to the possibility that the guests might realize the flaw in their request and rearrange their plans to enlist a trusted babysitter at home and enjoy a weekend away from the kids.