I have a MySQL table defined:
File
--------------------------
ID int(11) PK
name varchar(100)
customerId int(11) FK
i
MySQL perfectly supports unique constraints.
It does not support partial constraints/indexes, though, so you would need to mark non-primary images with a NULL instead of 0.
ALTER TABLE file ADD CONSTRAINT ux_file_customer_primary
UNIQUE (customerId, isPrimaryImage)
You can insert arbitrary number of NULL values into isPrimaryImage but only one non-null value per customer.