As of yet, there are very few DS(i) mode homebrew installable on the 3DS - the only two I can think of are that action replay alternative, and that launcher for blocked flashcarts.
NDS games are made to executed exclusively from a cartridge. I'm not a developer, so I don't know how hard it is to bundle a .nds file into a .cia, but clearly it's not very straightforward, or there would probably be a converter by now.
Not to mention that the only practical and legal DS(i) mode homebrew for 3DS will probably involve passing code execution to the cartridge, something that DS programs are absolutely not made to do.