Pocketnes
Pocketnes is probably the main emulator of NES games that people like for the GBA.
You can try the new tool for it if you want
http://gbatemp.net/threads/release-ez-flash-iv-aio.370132/
If that does not work then we can return to linking up guides, the EZ4 does do better if you give it a slightly modded version that kuwanger made.
http://ezflash.sosuke.com/viewtopic.php?f=12&t=12660 has more there.
HVCA is the other main emulator for NES games. For some things it did do better.
http://wiki.pocketheaven.com/index.php?title=Hvca
If you absolutely must use the classic nes/famicom mini series and not an emulator (really just use the emulators) then you will need to patch them -- they are some of the few games on the GBA to have anti piracy. That link on filetrip is a group of patches for all the classic nes games and those famicom mini games that needed them.
Find the right IPS file for the game you are using, load up the ROM in a IPS patcher, load up the patch, set the output and use it however you will. It should work on something already on your card and it should work if you have not patched the game with EZ4client yet. GBATA is a basic patcher but a nice tool to have if you are starting down the path of GBA emulation and flash cards.