I would argue that "coffees" as a plural is also correct, and would never be marked incorrect in an exam. A similar situation is with the noun "stadium". It's plural is stadia, or stadium. Both are good. It's very common to say "I've had three coffees today".

When we speak, we can make many mistakes intentionally. It is still correct to say "Two coffees, please" and it is faster. But "Two cups of coffee, please" is more correct from the formal grammar point of view and it's more universal to learn this pattern rather than the spoken one.