You can create the same sort of question in Swedish by using intonation, Det finns inget kaffe? However, that is not the sentence you're translating here, so you should use the normal question form Is there no coffe? or Isn't there any coffee?
"Isn't there any coffee?" was my first answer but it was not accepted as being the correct answer. It only counts "Is there no coffee?" as the correct anwser which is weird to me.
We're sticking to question-oriented word order in English translation so as to make a point of the inversion of subject and verb.