What ARE you using daycare for?
Generally speaking, daycare should be used when the parents are unavailable to care for the child because of other commitments. If you are using daycare, and you expect your ex to pay for it, you SHOULD be utilizing those services only when needed, such as when you are working. You SHOULD NOT be using daycare for things like personal time unless absolutely necessary, such as if you have a doctor's appointment.
I get the impression that your ex may not so much have a problem with paying for daycare, as much as he has a problem paying for daycare when YOU should be spending the time with your child instead. As a parent, and especially as a single parent, one makes sacrifices of their time so that the child is cared for. If you are spending a lot of personal time outside of work, and putting your child in daycare while you do it, that's a problem -and I could understand if he takes issue with it. It's not his job to finance your "me" time. I'm sure that the court order wasn't written with that intent.