Download play (as in the other person does not have a copy and plays like that) in games is usually a separate file, or indeed ROM (usually either utility.bin or another that escapes my mind right now. Either way you open them up like another DS ROM). They are signed so your partner DS will need flashme or whatever the equivalent is for the DSi and 3ds, or I believe the signing was beaten a while back so you get to do that.
Most people have flash carts to play with these days though so that is probably the better route. Should be no signing issues for this one as it is just position data and the like that is being fired back and forth so the DS/people making the game probably did not care and are unlikely to put any protections in place.
In that case I don't know what people have done or the various tools to edit the levels will do for this. I would probably start there though with
https://nsmbhd.net/ being a reasonable place to start looking. In most cases* you will both want to be running a modded version of the ROM and play as you will.
Even if there are no explicit multiplayer level editors I would still look at the level formats as it is unlikely the devs made a radically different format for such a thing and you can probably get something done/figured out what is already known.
*for some things you might be able to say host a game with a modded ROM and have it select a custom track order or timings that are within parameters but not officially selectable. If you are going to be doing custom levels though then you potentially end up running different levels/tracks and then weirdness happens, though some like that and if it is not competitive as much as timing and maybe the odd spiked item thrown the other way you could have some fun there (especially if one person is that much better and you can effectively handicap them).
