You can program it through RS-232
after you've programmed a bootloader into it.
Are you looking at AVR's for your microcontroller? (You may have said that already, but I didn't see it) Many AVR's use the same pins for SPI as they do for ISP. Although they might be on the same pins, they are very different, so don't get the two confused. I got them confused on the ATMega128 and ended up not being able to program my part
SPI - Serial Peripherial Interface - Used to communicate with many types of devices such as EEPROM, sensors, keypads, other microcontrollers, etc
ISP - In-System Programer - Used to program the MCU while it is installed on a circuit board. In the case of the AVR, these pins may be shared with the SPI port.
It is OK to use EEPROM on the SPI port and use a programmer to program the device on the ISP pins. You should have your ISP connector run directly to the microcontroller and tie the pins through resistors to the EEPROM chip. Don't forget a pullup on your EEPROMs chip select so that your programmer doesn't give it a ton of bad instructions while its programming the MCU.