There is a Wiibrew-like wiki for the DSi here (link below) if you want more information. But there is a "hack" :
Wintermute have released DSiLink which allow to send homebrews to your DSi and play them in DSi mode (but audio and touchscreen are not working). This thing works with a hack of the save of "Cooking Coach" and "Classic Word Games " which are hybrid games (special features on DSi and normal game on DSLite/Phat).
http://dsibrew.org/wiki/Main_Page