Under Your shop, Marketing, write an email to your own customers. Choose who gets it from what FullDiary already knows: everyone with an email address, people who have not been in for a while (say 90 days, with nothing booked), people who came recently, or anyone who has had a particular service. The page tells you how many that reaches before you send.
Write the subject and the message in your own words. {first name} and {shop} fill in as it sends, and the email as a customer would see it sits beside the words, with your logo and photo if you have them switched on under Emails. A Book button is added for you, pointing at your booking page. Put a discount code from Sell more on it and the button carries the code, so nobody has to type it.
Send me a test sends it to your own address. Send asks once, naming how many people it goes to, and then it goes. Afterwards the email's page shows how many were sent, how many booked through its button and what those bookings are worth, and Send again copies it into a fresh draft.
When you cancel a booking in the diary, the message that follows has a Fill the gap button while the time is still ahead. It offers the freed time by email to the people most likely to take it: the waiting list for that day, anyone who has had that service, or anyone in during the last 90 days, with a count beside each. The message is started for you ("A space has come up at {shop} on Tuesday 28 October at 2:00pm. Book it before someone else does.") and the Book button opens your booking page on that day with that person and service already picked, so the first to book takes it. It shows under Marketing like any other email, as "Gap on Tue 28 Oct at 2:00pm".
Your customers can stop your offers with one tap on the link at the foot of every email, and you can switch offers off for one person from their booking in the diary. Booking confirmations and reminders still go as normal. People who have booked with you may be sent your offers until they say otherwise; every email carries the way out, and nobody who has stopped them is emailed again.
Marketing is an add-on to Pro: 9.99 GBP a month for your whole shop, however many people work there, or 99.90 a year on a yearly plan. Add it under Settings, Your plan, and stop it whenever you like; the unused days come off your next bill and everything you sent stays. It is not available yet on a plan bought in the App Store or Google Play.