I have an app that allows the user to view, manipulate and manage a collection of Schedule objects. Different parts of the app need access to this data. I\'ve experimented with
If you've got a central data model that needs to be accessible to multiple controllers, there's nothing wrong with using a singleton to manage the data-- a "sharedManager" is exactly what the scenario demands. This is essentially what Apple does with their address book API for manipulating contacts. They use a C-style API but it involves getting a reference to the shared address book database and then using that in future calls.
Using the app delegate works too, but as you note it's really the same thing. You're designating the app delegate singleton as the owner of the data model, which is OK too.
NSUserDefaults can be abused in this way but that's really not its purpose. Aside from being kind of ugly, it also puts restrictions on the type of data you can store. Your own model can store whatever data you like, but NSUserDefaults is not quite so flexible.
Using SQLite or a property list or whatever to store the data to a file is really orthogonal to the question of how to manage it. From your description a singleton approach sounds reasonable, and that singleton can write to files in whatever way makes sense for the data you're working with.