The first thing you need to do is look at the capacity, acceptable current, and discharge voltage curve of the coin cell. Gut feel is that you're not going to get any significant operating time. I suspect that you're more in LCD territory.
You really need to provide more detail before anyone can help. What sort of display are you looking for? The number of single dumb 7 segment displays is almost endless (you are shooting yourself in the foot a bit by looking for a 4 digit one). Are you looking for something with a built-in decoder of some sort, or one that you will multiplex drive from microcontroller pins?
Edit: Sorry, my brain read LED for some reason. Reading your other posts, it looks as if they may all related to a single project. It would be helpful if you kept them all in one thread to allow people to understand the context.