is "a coffee" grammaticaly correct?...why?

[kenji]

i am teaching grammar...
i am very much bothered by this sentence in our grammar book (intermediate grammar by raymund murphy) explaining the use of some nouns that can be countable and uncountable...
the other examples were fine except for "I'd like a coffee" to refer to a cup of coffee......if this is grammatically correct, would "a milk", "a water", etc. do?

[RonBee]

The phrase "a coffee" is sometimes used as shorthand for "a cup of coffee".

A coffee can make you forgetful

BBC NEWS | Health | A coffee can make you forgetful

(Capitalization.)

~R

[RonBee]

The word "waters" (for "glasses of water") is restaurant lingo. I suppose that milk(s) can be used that way too. Outside of that context, however, stick to "glass of water" or "glass of milk".

~R

[Ouisch]

"A coffee" is rarely used in AmE. When ordering a cup of mud, we'll say "some coffee," "a cup of coffee," or sometimes simply "coffee." About the only time we preface it with "a" is when we order one of those designer coffees from Starbucks: "I'll have a double espresso" or "I'd like a half caf lattee with extra foam and a whisper of cinnamon."

[Tdol]

In BrE, 'I'd like a coffee' is common.

[rewboss]

Often there are times where uncountable nouns can become countable. "Coffee" is one, but there are many others:

chocolate: I like chocolate (the sweet, brown or white substance that melts in your mouth); I like chocolates (the small, individual pieces of confectionary based on chocolate)

beer: I like beer; I'd like a beer (a pint, a bottle or a glass of beer)

potato: Have some mashed potato (the potato is all mashed up together so you cannot tell one potato from another); Have some roast potatoes (you can actually count the individual potatoes)

light: We need some light in here (it's too dark, we must illuminate the place somehow); we need some lights in here (individual light-bulbs); it was such a beautiful light (the light had a specific quality to it)

paper: I need some paper to write on; I'm going to get some papers (documents; or as a synonym for "newspaper")

There are many, many more of these. In fact, I think most uncountable nouns can be used in countable contexts, although often the meaning changes, usually subtly, sometimes radically.

[MikeNewYork]

"A coffee" is rarely used in AmE. When ordering a cup of mud, we'll say "some coffee," "a cup of coffee," or sometimes simply "coffee." About the only time we preface it with "a" is when we order one of those designer coffees from Starbucks: "I'll have a double espresso" or "I'd like a half caf lattee with extra foam and a whisper of cinnamon."

That is regional in the US. In Chicago, we almost never said a coffee, but it is very common in New York.

[MikeNewYork]

i am teaching grammar...
i am very much bothered by this sentence in our grammar book (intermediate grammar by raymund murphy) explaining the use of some nouns that can be countable and uncountable...
the other examples were fine except for "I'd like a coffee" to refer to a cup of coffee......if this is grammatically correct, would "a milk", "a water", etc. do?

You'll encounter differences of opinion on this. For many, "a coffee", "a milk", or "a water" is incorrect. However, there is precedent for the countability of individual servings of liquids:

a Coke
a whiskey
a soda

For now, I would call most of these constructions informal/colloquial.

[Ouisch]

That is regional in the US. In Chicago, we almost never said a coffee, but it is very common in New York.

(in best Johnny Carson voice) I did not know that.

[MikeNewYork]

(in best Johnny Carson voice) I did not know that.

New Yorkers also "get on line". They're weird.