It depends on the sentence.
If you say;
Coffee is bad for you.
Coffee comes from Brazil.
Can I have some coffee?
the word 'coffee' is uncountable. It is a singular noun with no article.
However, if you say:
'There are many different coffees for sale in that store',
you mean different types of coffee, so in this case it's a plural noun, and therefore countable.
and if you say:
'How many coffees did you order?'
you mean 'How many cups of coffee?', so here again you are using the word as a plural noun, and it's countable.
So you can say either:
'Can I have a coffee?' (countable, meaning a cup of coffee)
or
'Can I have some coffee?' (uncountable, meaning an unspecified amount of a liquid)
So, as you can see, either is possible, so long as the internal grammar of the sentence is consistent.