Nice project!
A typical CR2032 ( I checked the Energizer datasheet) has a self discharge of 1% / year and a capacity of 240mAh, so that's a self discharge rate of about 2.4mA/year, or about 6.6uA per day. The ATmega328P at 3V in full power down with watchdog disabled has a supply current of about 0.6uAh (datasheet page 603). That equates to 14.4uA/day or twice the self discharge of the coin cell. Still excellent and I suppose the coin cell might last a few years if you keep the size and frequency of the transmitted packets low :)