You need a special item. It is an event item. If not you can use an action replay to get it. Here is a link to tell you exactly how to get ALL legendary's and the other too.
Here is what it says about Darkrai:
Once you obtain the item Membership Pass at the event, Go to Canalave City and you will be able to access the Motel which has previously been locked. Go there for a night's sleep and you will be disturbed by Darkrai in your sleep. When you wake up, a Diary will be there which contains Darkrai's location. Go to the Sailor at the bottom of the city and he will take you there. When you get to the island, you can go up and battle Darkrai. It is at Lv. 40
But the event passed, sorry :(