The clients can setup their timezone. When a prospect schedules for the first time in your calendar, they will be presented with a timezone pop-up window requiring them to select their own timezone. Existing clients can check and change (if needed) their timezone from the Calendar page or their Profile form on the private portal. You as coach can also check their timezone in their Profile tab on your end (CONTACTS TAB > Contact Name > Profile tab > section "Client Information").
Provided that the timezone is set correctly for the clients, they will always see your calendar available times and their appointments with your in THEIR timezone, not yours as coach. The appointment confirmations and reminders sent to the clients will also display the appointments in their timezone (the system converts the timezones automatically for clients with the replacement tag$APPOINTMENT_TIMEZONE$ used in the confirmation and reminder templates).