If you are with an agency why are they not placing children in your home? Are the private rates you are charging in line with what the agency charges? Also while it might be common for parents to not work a full week if you were available for the full week but allowed parents any 4 days you might get more interest as businesses are open all days and therefore different parents will have different days off. If you are not open on Friday for instance you are missing out on parents that are off Monday but need Friday. It may also be that their days vary so on any given week need to use the day you are closed so don't contact you. A teacher would work the full week would they not?
It does go in waves and generally picks up with back to school especially if you want older kids. At this point I would be inclined to change my open days and offer what will appeal to the greater number of parents and then over time switch to your ideal. Any time you are restrictive you severely limit your clientele.