Acuity doesn't have a built in automation feature but if you're interested in sending clients a birthday email or coupon for their birthday, then we have a great workaround for you!
You can include a birth date field in our fully customizable Intake Forms and additionally make that field required for clients when booking an appointment! While there isn't a built-in field for birth dates, you can use the Textbox field to gather this info!
Next, you could export your client list which would include their birthdate and then import that into an email marketing platform such as MailChimp--whose Automation feature is completely free!