I know this is an old post... just thought I would weigh in!!
I charge my full time spots on a monthly basis (that is, as of now, $600 per month). If someone wants part-time, they actually pay more if you look at daily rates (p/t pays $40 daily). I have 2 different arrangements; 2 families pay me a set amount per month, which guarantees them a set number of days. They basically tell me what days they need, and a spot is available. If they need more, they pay more. If a family doesn't want to pay a specific amount, they pay me daily at the end of the day (and they take a chance when booking that I may be full that day). I find this works for the most part.
As for the dilemma (that I hope you have sorted out now), I have been there. I was doing after school care for a friend. I ended up discounting my regular rate for her, significantly, because she said it would only be for an hour or so daily. Well, wouldn't you know, it turned into an hour and a half to two hours, daily. Then he would go for a long stretch where he was sick/absent/on vacation and not coming, and there were all sorts of hints about me charging even less. I didn't say a word, just kept collecting regular fees. I know she's a friend, but it's still a spot (that could be filled by someone who WILL pay the regular rate), and it's my budget on the line here. The end of the story is, she no longer uses me for regular care, just drop in. No hard feelings, she just didn't want to pay what she needed to maintain her kid's availability in my childcare. Oh well.