Surely I want a coffee is the correct translation here - even if you want to practise the number one. I'd only say I want one coffee if it was part of a list eg one coffee, two teas.
coffi - a coffee
un coffi - one coffee. As you say, as in 'one coffee and two teas, please'.
I have to use it often - when we go out as a couple it is only me who drinks coffee, so I usually have to specify un coffi to avoid ending up with two and sending one back!