You can ask your friend who has download the mission but yet to do it to send the mission to you.
Or the second way: Use some device to transfer the save file with 2 mission in the job list (that you can find somewhere on the Internet) to a
rented copy of the game (or any Time/Darkness cartridge that is safe to erase the save file). Then turn on 2 DS, one with your current game and the other with the rented one, and start transferring.