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Problems: Must be updated frequently to be useful. This isn't an optimal solution to the scheduling problem and still has no way to leverage certain private information. This does facilitate joint-babysitting scheduling. This also allows better coordination of flexible schedules. 
Storyboards
Design 1: This design will have three main sections organized by tabs: Home, Profile and Jobs. The Home tab will show notifications that the user receives. The profile tab will store useful information about both types of users, and also allow babysitters to store their availability. The Jobs tab will allow parents to create new jobs and allow babysitters to manage the jobs they have been invited to. The major feature of this design is a calendar interface that allows users to quickly display their scheduling preferences by painting over times which work for them.
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Design 2: Timeline
Parents create events which they need babysitters for and babysitters specify availability. These are done with sliding bar timelines broken up by day. The sliding bar makes it very easy to specify blocks of time one is needed. Since these are thin, we can stack many of them above each other, and then checking whether someones schedule matches is just a matter of looking down to see if those blocks overlap. This makes checking for compatible times very easy. We also allow sorting by availability or preference, to make it easy to find a match or pick your preferred babysitters. Unfortunately it limits the amount that can be displayed, which is why we have a toggle for which day is displayed. The toggle buttons are partially filled/colored to show roughly how many matches occur on that day. 
Use: Two parents decide they want to take an evening off to see a movie. They decide on their preferred times on Saturday and make an event on Saturday in SitterPlanner. They decide to sort their babysitters by preference, and quickly notice that their two favorites are not available until later in the evening. They could go with one of the other babysitters they trust, but this time, they decided to go to a later showing so their favorite babysitter can watch their daughter.
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Design 1: This design is very efficient because painting over all times which work can be done very quickly. It might be a bit confusing to learn without text explaining what to do for at least the first time. It is somewhat safe since there is an easy method for undo-ing mistakes, but mistakes will be very common because any time a user accidentally drags across a time with the mouse down it will get colored.
Design 2: This design allows efficient input and very easy schedule comparison on single days. Since timelines are thin, we can stack many of them on top of each other and visually looking for overlap is relatively easy. We can also prioritize the list based on availability, favorite babysitter, or other criteria. This does not handle multi-day scheduling well. Creating multiple blocks of time may not be the most intuitive in this interface. We also believe this design will tend to drive babysitters putting up their schedules and parents using it to find a match. This achieves the parents goal very well, but does not allow babysitters to coordinate with multiple parents over flexible schedules.