"A coffee?" means "Kahviko?". It's nominative, indicating a single countable unit. "Kahviako" uses partitive, indicating that there is an amount, not a unit. As a mass noun, "coffee" without an article serves the same function.
Edit: I should make the slight correction that "a coffee?" actually translates to "kahvinko?" in this particular linguistic context. It should not be in nominative but rather in accusative case, as it is a total object due to being an entire countable unit and the target of a verb, which in this instance is "haluavat".