How to do it...
the 8051 does not care whether it runs from PHYSICAL ram or rom,prom, eeprom, whatever...
However, if it is running from RAM, there must be a way to put code into the ram, so you must at some point be running from rom,prom, eeprom. And that point has to be from address 0, the reset vector.

One simple way is to use the highest address bit to choose between ram / rom, select rom for low addresses, ram for high addresses. This way you can use the rom to load code into the ram. The ram can then re-write the "eeprom". But you will have to avoid interrupts, since the vectors are at 0.