I considered making an SD-based NES cart at one time, but upon further research, I found out it's incredibly hard because of the mappers. The game expects a mapper to exist -- it even writes to the thing. You can make your own mapper with something like a microcontroller or FPGA, but some mappers are fiendishly difficult to emulate and they can require tapping into every pin on the connector. RetroZone makes the
PowerPak, which uses CompactFlash with an FPGA, but it's kind of expensive at $135 USD. I read a story from the guy who designed it and he had many things to say about the difficulty of building one.
However, it's much simpler to make a single game. You can hack up an old game (reusing the mappers) and replace the ROMs with EEPROMs, if you have access to a programmer. I was hoping to do this and use a microcontroller on-board to reprogram the cartridge over USB, but I found it ridiculously difficult to get info about how to program the EEPROMs; apparently every manufacturer has their own proprietary protocols which the programmer manufacturers have to pay for.
At the end of the day, I'd recommend putting a socket on an existing board and using a real EEPROM programmer if you just want to get a game up and running. For anything else, the PowerPak is probably the way to go; even for the price, it looks to be cheaper than doing it yourself.