It would not be "customers" because if it was plural it would be "customer's" but as to "customer's" vs "customer" I do not remember actually (I am native, its just so native you don't really remember it) I want to say however, that it is "customer parking."

"Customer Parking" is better. Do not worry about any plural or apostrophe.

*I meant it's just so common you don't really....

"customer parking" When you use a noun like an adjective-- to add more information to another noun (in grammar it is called a "noun adjunct" or "attributive noun") it is usually singular.