"I don't have either tea or herbal tea, but I have coffee."
Translation:Je n'ai ni thé ni tisane, mais j'ai du café.
You don't usually use indefinite and partitive articles with the negative conjunction "ni"; "du café" is not being negated.
Came to the discussion with THE TWO questions that others have...(a) why is the partitive(or definite) articles missing unlike other examples....(b) why is prendre rejected? Answer #1: It is always OK to put the ARTICLE..(DUO does accept it as MatthewB6 posted) BUT when the nouns refer to 'uncountable/bulk' items like tea or beer or coffee then you can(maybe should) leave out the articles. Here is a link of how to use ne..ni...ni from the reputable LAWLESS with an example using tea and beer in the quiz. https://www.lawlessfrench.com/grammar/negative-conjunctions/
Answer #2: (why not prendre) Look no further than the man on the bike "nigeranoma" elsewhere in the posts.. for a brilliant piece of deduction..I am throwing a lingot his way.
See the posts by nigeroma, yours truly, and also this link https://french.kwiziq.com/questions/view/avoir-vs-prendre.
While the verbs may be loosely interchangeable prendre means to actually be in the process of 'having' the food item or at least ordering it ....