99% of the time you would be encouraged to go flash cart, mod chip, firmware mod (if it exists in a useful capacity for your chosen console) or emulator.
The Read Only Memory part of ROM tending to be what speaks to that.
As with most things the everdrive is the king of the hill for flash carts, GB/GBC being no different where they have the everdrivegb. If you wanted there are also good emulators on the GBA (and anything that runs a GBA slot) so you could use a GBA flash cart (which are considerably cheaper and also do GBA) there and emulate on that.
There are further quirks with various cheat engines, exploit loaders (see smash brothers for the wii) and quasi flash carts (there are things that dump the game into RAM or intercept reads, apply your patch and present that to the console). Nobody here encourages the use of such things over a flash cart and the rest of the list from the first paragraph.
As you asked though it is possible in this case to buy a game, swap out the ROM chip with another compatible chip and go from there http://reinerziegler.de/readplus.htm#Home%20made%20carts
Really though get a proper flash cart or content yourself with emulators.