Can you play Dixit cooperatively with only 2 players?
That doesn't sound too bad, except that the drawn cards could be really off.

Alternatively, you could try to play a cooperative variant.
These two are interesting:


  The game is cooperative. Each player is the storyteller five times for
  a total of 10 turns and you go for a high score. The highest possible
  is
  70. 
  
  Neither player has a hand. Each turn, the storyteller makes up a story
  without seeing any cards, and then six cards are flipped over from the
  deck and arranged. Both players (must?) vote for two cards that they
  think best match the description, and color matters: use the red peg
  for your 1st vote, and the green peg for your 2nd vote. Then players
  reveal their votes. 
  
  For a card where you both voted red, you get 4 points. For a card
  where you both voted green, you get 3 points. For a card where you
  both voted but the colors didn't match, you get 2 points. For a card
  where only one player voted for it, you lose a point.


Source: https://boardgamegeek.com/thread/700350/2-player-cooperative-dixit


  How to Play
  
  
  Deal cards to each player as usual.
  Pick a scoring marker for the players (just one marker) and another as a failure marker.
  Pick a player to be Storyteller first. I'll refer to 'Storyteller' and 'Player 2'.
  The Storyteller picks a card from their hand and gives a clue or tells a story about it, then places the card face down.
  Player 2 picks a card from their hand to try to match the clue.
  Add 4 random cards from the deck to the chosen cards.
  Shuffle them out and places them on the table as usual.
  Each player now secretly makes a guess. The Storyteller wants to find Player 2s card. Player 2 wants to find the Storyteller's card.
  
  
  Reveal your guesses!
  
  If you both guessed the other player's card correctly, cheer and
  advance your scoring marker 1 space.
  
  If either or both of you guessed wrong, pout and advance the failure
  marker one space.
  
  Each draw a new card. If you still have 4 cards left in the deck, swap
  who is Storyteller and proceed to another round.
  
  Try to have more points than failures at the end of the game!
  
  What does this mean? When you are the Storyteller, you want Player 2
  to guess your card. This is easy. You could just say "A city made out
  of eggs", and your partner is sure to guess it.
  
  But...you also want to guess Player 2's card. Give a clue too
  specific, and your partner won't be able to play any card you can
  recognize!
  
  You need to give them enough room to play a card you recognize,
  without making it too easy to be fooled by a random card.
  
  Spirit of the game: No giving "double" clues that are meant to
  describe your card and the card Player 2 is supposed to play
  separately. ("My card is a scarecrow, but your card has plants").
  
  No setting up codes.
  
  No repeating clues.
  
  Remember, you are trying to play a 4+ player competitive game as a 2
  player co-op. Try to break the game and it will break. Go with it and
  have fun and it should provide some amusement. I've tried to make it
  resistant to "casual" abuse at least.


Source: https://boardgamegeek.com/thread/676496/2-player-co-op-dixit-variant