Unique IDs for physical modules added to a circuit
I agree with Alex's suggestion of using an EEPROM but I would get one with a unique serial number already burnt on it. Such as Microchip's 24AA02E48 (datasheet Here). It has a 48-bit globally unique ID or there is a 64-bit option if needed. They are in the $0.20 price range.

Plus you have the EEPROM to store future additional data, like batt. charge cycles, etc.