The recommendation will vary widely depending on where you live and how things are typically done in your community. I would recommend charging the local rate for a nanny. Where I live (high cost of living), a nanny or sitter for 1 child is roughly $15 / hr, 2 kids $18 / hr, 3 kids $21 / hr, 4 kids $24/ hr. Parents pay all incidentals and provide all food. So a mom with 1 kid taking on a second kid as a nanny would charge the nanny family $18/2 = $9/hr. A mom with 3 kids taking on a 4th as a nanny would charge $24/4 = $6/hr.
Based on the cost of camp in your area, your local babysitting / nanny rates are probably lower, but the same principle / scaling could apply.
I'm sure other will suggest other fair ways to charge, but this is what came to mind for me.