I want to be able to save the clock position in EEPROM if the power is failing, like when your changing the batteries. The DS3231 has its own battery backup and has a "/RST" signal that it can assert when it's detect a power failure so I just need to be able to provide power to the ATtiny85 long enough to write position status to the EEPROM.  I'm thinking of something like this:

Where ATVCC is the VCC pin on the ATtiny85.  The Diode should isolate the power to the ATtiny85 and the capacitor should supply power long enough for it to save the current clock position to EEPROM.