a. (Please) bring me a cup of coffee.
b. Can you please bring me a cup of coffee?
c. Could you please bring me a cup of coffee?
Spanish girl: Can you please bring me a cup of coffee?
English girl: Yes, I can, but I'm not going to. Get it yourself!
Even with the word "please" in the two first options, the English people may sense a slightly commanding tone in them, so, for example in the second case, they would be tended to say
"Yes, I can, but I'm not going to. Get it yourself!".
So, the last is the best option (c)...
That would be the polite way you could ask for a coffee...
source: wordreference.com