Agreed, it really depends on what YOU can live with here. Personally, I always have a few part time families because they pay more daily, and it means that some days are lighter than others.
If the schedule is always changing, then it will make it very difficult to fill in any days around that family. But if you know exactly when they will need care, it may be possible.
You could offer them a full time rate, and let them know that if they need care on the 5 or so weekdays that they are not using, that they just have to let you know?
My full time monthly fee applies to 4-5 days per week, and they are not that far off.