Follow these steps to setup a membership program that provides x amount of appointment bookings (primarily for a free booking as you can use vouchers and get items for paid bookings):

1. Setup the credit block by going to Manage Credits (under sell) and then click on New Credit Block
2. Set the component type to Appointments, set the number of credits and then set for subscription based.
   
   
3. Setup the membership program and the billing service that is associated with it.  When setting up the billing service, make sure you select the new credit block you created.

Now when someone subscribes to that membership program, they will receive the number of credits you entered (in this case 10).   Each credit will be utilized upon a successful appointent booking or reservation.  Once they utilize the last credit, on next booking, their credits will replenish (unless you have auto-renew disabled on the service).