It depends on what you mean by "simple" for your "simple circuitry"

If you want to do it from hyperterminal, then your "simple circuitry" would need to convert from RS232 to whatever serial arrangement the EEPROM uses (I2C, etc). You could do that quite easily with a cheap, low-pin-count microcontroller.

Simple EEPROM programmers turn up very often in the "Circuit Ideas" sections of electronic magazines - loads of people have suggested ways to connect to the PC's serial or parallel port, usually with a free download of some simple software.

You'd probably even find such stuff in Application Notes from the EEPROM vendors - have a search around their websites.