The sentence is asking about a non-countable noun (coffee) in a question. For non-countable nouns in questions or negative sentences, 'much' or 'a lot of' are typically used. 'Many' is used for countable nouns. Between 'much' and 'a lot of', 'a lot of' is often preferred in informal contexts and can be used in questions. However, 'much' is also grammatically correct here. Given the options, 'a lot of' is a common and appropriate choice for this type of question.