"Do you want to drink coffee or drink tea?"
As it is a question you should you the question word "ma" at the end of the sentence. 你想喝咖啡或茶吗？
I wouldn't use 吗 in this case because that would imply "Would you like to drink coffee and tea?". This question you can answer with "Yes, please." It's the same as "Is your baby a boy or a girl?" being an ambiguous question, to which you can answer, "yes, my baby is either a boy or a girl."
Whereas 呢 seems to give more of the meaning of "Would you like to drink coffee instead of tea? (and vice versa)". This you might answer with "Tea, please." or "Coffee, please." But I'm no linguist/ translator so... discussion appreciated!
In this sentence you should definitely include either a 吗 or a 呢 for it to be a question though!