The discount code could be set to apply only on some chosen sessions.
From the school coordinator's dashboard, please go to left menu, then Student Registration setup, then Add Discount Codes.
When setting up a new code, please choose "Only Sessions Selected Below" as shown in the attached screenshot, then select providers and sessions to apply the code to. Then the code would only be applied to the selected sessions.
We can't assign a discount code just for one or some users. But the code itself should be private, only the parents who are authorized to use the code should be emailed.