"Do you want black tea?"

Translation: Chcete černý čaj?

[esamota]

I now see it was tea not coffee, so that could have been why the answer wasn't accepted :D. "Daš si černý čaj?" would have probably been accepted.

[ion1122]

I would translate your sentence as "Are you having tea?"

[VladaFu]

I would as well. This is not a phrase book, you should learn how to compose sentences and translate them quite closely. In facet the question may be asked in a shop, not just in a restaurant.

[AgnusOinas]

"Dáš/dáte si černý čaj?" is definitely a very natural way of asking someone "Would you like black tea?", when you refer to actually drinking a cup. On the other hand, "Chceš/chcete černý čaj?" is a better question when someone wants to give/sell a pack of black tea leaves/bags.

[esamota]

I don't understand why "Daš si černou kávu?" isn't accepted as a correct answer. As far as I understood from my Czech teacher and friends, they do not use "chtít" when asking about food or drink.

[ion1122]

I believe it is common to use "chtěl bych" = "I would like" when talking about food & drink. Maybe your teacher meant only that it is more polite to say "would like" than to say "want".