Help writing an Counter Offer Proposal Letter?

Finance guys, need some advice:

I've gotten an offer for my dream job, only the salary isn't close to what I wanted - especially for the work they'll want from me. My current company is likely to counter offer and with the job being in one of the most expensive places in the US to live, I need some help on how to go about writing a counter offer proposal letter.

I'm in a unique position in that I'm not in any rush to leave my current job and the $$ has to be perfect to make me even consider it. I really love the company (and the city it's in), though, so I'd consider this a great opportunity.

The articles on the web are at least 4-5 years old. Have any of you had to do this before? My biggest question is how you start one of these, and keep it positive while asserting what your salary needs are.

Does showing "research" I did with those cost of living calculators worth anything, or are those numbers already wildly skewed because of differences in cost of living around the country?

I've got until the end of next week to let them know, so there's no rush, but the sooner we can get negotiations going, the better. Thanks for any help you guys can give!