Hyperterminal is all you need.

From the [Transfer | Send Text File] command, it actually sends a binary file. It just uses the default .TXT extension. But you can pick any file.

In the [File | Properties | Settings Tab | ASCII Setup Button] you can add the delays required to give the PIC time to write to the EEPROM, 10ms or more "Character Delay" depending on your EEPROM. Then you don't need any complex buffers or flow control.

It can be received on the PIC end with SERIN(2) or HSERIN, and stored to the EEPROM byte by byte.

hth,