this is why i made a deal with my mother. She gets me a DS Lite, i give her my old DS. Two gifts with a ten dollar difference. Saves us both money, really.
So, try convincing others to have your old DS first, so you wont have people say 'awww, i wanted it!'. If no one else wants it, then see the prices you can get when you sell it to EB Games or Gamestop.
Or, another idea, if you find a game you want for your DS at a Gamestop or something, you could excxhange for money at the game.
And, for last, try eBay. You DO have to have a credit card because of Paypal, i believe, but you can sell the DS at little or the same price as you got it (and in some cases more)