How are private one-on-one lessons handled?
Like any other class, only with a capacity of one. A private class has its own schedule, teacher, and session pack; attendance deducts a session, an excused absence grants a make-up right, and the invoice comes from the same pack.
A credit pack usually fits best here: the parent buys ten meetings, the balance drops each time the student comes, and rescheduling demands no manual arithmetic because what is counted is sessions, not dates.