In my opinion, "can you" is a more polite, but "could"/"would" is even better. But normally when I ask people for favour, I just say "can you...?" It's totally fine. However, when I am working and talking to the customers, I say "would"/"could" most of the time. And I rarely use "will" when I ask for favour.
I totally agree. In my humble opinion that would be the best answer to the original Q, especially if it is followed by "please".
Joelline is quite right by saying
Yes, it does assume that the person is able to do something, but "will" and "would" are more polite because you are asking if someone is willing to do you the favor: it sounds as if you are giving the person a choice.
The key here, is the word "choice".
I would go a step further. In England, if someone wants to be
very polite, they could say "would you be so kind as to bring me another cup of tea, please?"
Yes, it is long-winded, but it gives the other person the choice (so you are not pressurising them into doing something they might not want to do), and you also indicate that by doing so you would consider it to be a kind gesture on their part.
The funny thing is that if they wish to refuse, they could look 'unkind and mean' to other people, which 'pressures' them (
ever so softly and politely) in doing what you want them to do in the first place

. That's what I call English ironic politeness (my words…).
I hope this helps rather than confuse. I realise you might be wondering about the "as to" in the sentence; rather than a long explanation, it's best to have a look
here.
The short answer to your Q, Brave Heart:
Would you bring me a cup of coffee, please?
