Unlike Quake 1, there is simply no way of fitting Quake II into the memory configuration of a stock DS. To play the game you must have a supported slot-2 flash card that contains a minimum of 16 megabytes of RAM.
Supported cards:
Note: the game will not run without a slot-2 RAM. There will never be a version of Quake2DS that does not require extra RAM.
Slot-2 RAM is very slow and the performance of the game greatly depends on the speed of your RAM. Luckily some cards can be overclocked to improve the game's performance.
However, not all cards are made equal and cannot handle tighter timings. To more robustly find out if you RAM is capable of an overclock, please try memtestARM from Pineight.com
If you can overclock your card, make sure you choose one of the faster memory options when the game first starts up.
You'll still need to have the original games and some additional hardware to get them running, but they're worth investigating for yourself. Check them out here:
This is the binary for the first prerelease of Quake2DS