Iīd like to have a relaxing chat over (a) coffee with you. The only problem is if we should have it over coffee or over a coffee. You can find oodles of constructions with either phrases. Do the two belong to different varieties of English? Well, it wonīt spoil the coffee, anyway. So, you are welcome!
So, it does not have anything to do with British or American English. For instance, there is a similar distinction between the two varieties: to play (the) guitar / AE (BE). Could it be that one of them is rather the traditional and the other a new version. As just coffee without an article signifies a collective noun, I would have expected to have a chat only over a coffee, i.e. a cup of coffee. But if it is the way you say, I leave it up to you in what form we may chat.
P.S. Joking apart, I meant to write uncountable noun. In spite of the gaffe, both collective nouns, mass nouns (coffee without article and plural) (and in addition abstract nouns) - as they share similar features - fall under the same umbrella term (category) of singulare tantum.
Something else has come to my mind. It is not very likely - although not impossible - that the two versions have always coexisted, not even in two different varieties. So with some probability one may assume that one of them is older or the original one. Does anyone happen to remember? What makes me think so is inter alia the fact that coffee is an uncount noun here. Moreover, I have checked a number of contextual examples and have found out that most of the over coffee versions go with a second object like coffee and cake/biscuits. Could it be that the non-article version has its origin here?
And what if we choose a verb of speaking that goes with the preposition over instead of chat/talk? Then weīd have: We debated over (a) coffee. Wouldnīt the non-article version sound as if coffee was the object of the debate?
But you are, and that is what mattered to me. Last night I wrote for the luminaries only, just between you and me and the gatepost. You see, I havenīt changed yesterday`s approach yet. I keep bestowing gracious favours to whom it is due.
In actual fact, it is a terminus technicus in grammar. As far as the mass noun-meaning (I like coffee) is concerned, it is a singular noun. Coffees would mean sorts of coffee, but the two of us should rather chat over coffee (well, Iīd prefer over a coffee, and I feel deep inside, you do so too), not coffees. If it means cups of coffee, Iīd say one coffee between us at a time will do. More would be too much of a good thing.