Sorry don;t like it (speaking as someone in exactly the same position).
What's worked for us (but you need thick skin) is asking every parent waiting to srop off in the morning when they would like to help out, and not taking no for an answer. If mum says no (OK stereotypical that it's usually mums dropping off, but true) then ask about Dad, nanny, grandparents. If no childcare for younger kids have ready name of other parent with similar aged siblings who can swap babysitting, if still no then ask to wash tea towels/count Tesco vouchers/print out fundraising publicity etc.
We do it at teh beginning of each half term, and whislt everybody probably thinks I'm a pushy cow I do have a full rota!