As documented here there is a property on the AppointmentRequest class for the CRM webservice that allows you to add constraints to what possible appointments are returned from a search.
The actual constraint is specified as an xml string, but I can find almost no documentation about it. Can any one point me to any relevant resources?
I was never able to find any quality documentation on this property or an accepted schema. About all that is available (that I've found) exists on this example from the SDK: Schedule A Resource
You can kind of see how you would limit the search results to a set of resources/users. The list of which properties can be replaced for "name" in the example is in the article ConstraintRelation.Constraints Property.
Hope this helps...