The configuration of Appointments is generally across all clients, but you've got several options by which to custom tailor the rules for client scheduling on a per-client basis.

To set this up for a given client, bring up their Client Manager (by clicking their gear icon as found in the Clients listing) and go to Settings >> Appointments.

There you'll find you can override the organization-wide setting for the client's self-scheduling.

You can also designate which specific Appointment Types the client can schedule, effectively overriding the per-Appointment Type setting of whether or not clients are allowed.