This is exactly why I ask for payment in advance, at the beginning of the month. I have had people that pay a couple days late, but have not had to get "tough" on anyone yet. I have a good batch of parents now that understand that this is my livelihood.
I agree that refusing childcare until paid in full is probably more effective than late fees. I mean, if they have already received the service, we don't have a whole lot of recourse at that point. If these parents have an issue, ask them if it would be ok if their employer held back thier paycheque without any notice!!