You only have 1K of EEPROM on an arduino. To make a stand alone system you need an external EEPROM chip. You then have two programs one to read data from the serial port from processing and write to the EEPROM and then you program the arduno with the other to do the replaying bit.
You can get I2C EEPROMs so they will sit nicely on the same bus as your D/A.