Coin cells are among the most polluting of batteries. If size and weight can be an issue you should probably go for LiPo batteries. A 1000mAH battery should do in that case, though you would need extra circuitry for the charging as well as for the regulating. A lineair 3.3v regulator just won't quite do the trick in that case with it requiring a minimum of 4v (and the LiPo will only provide that up to 70% of it's charge)