Without special power saving programming you won't power an Arduino long with a coin cell. Did you think about that?
offcourse , with all those unecessary items like the vregs in arduino it never going to last on a coin cell a special regime to shutdown unwanted perpherals on the chip need to be done and sleeping and wake on ext. interrupt needs to be configured im all prepared for that .
The Arduino already has such a feature on board (it automatically switches between external power and USB power)
AS you can infer for the nature of my imlication IM not using a full flegded arduino and never have! I always build by circuit based on the minimalist circuit to achieve the feat at hand so understand the fact that chip is on its own!