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Thank you GoofyStar for tipping us off to this Darkrai event! If you own a copy of Pokemon Platinum only, and not Diamond, and/or Pearl then this event is for you! Here are the instructions on how and when to get the Member's Card, so that you can visit Newmoon Island! These instructions were taken from serebii.net.

Japan: December 1st, 2008 to January 15th, 2009
America: August 3rd, 2009 to September 13th, 2009
Europe: 2009

• Get the National Dex from Prof. Rowan
  
• Visit the boy in Canalave City who suffers from Nightmares
  
• Sail to Fullmoon Island and confront Cresselia, when it leaves it will leave Lunar Wing
  
• Return to the Boy in Canalave, wake him up, then board the ferry at the Harbor Inn
  
• You can now visit Newmoon Island! Darkrai Waits for you here.

How to Obtain Member's Card
On the 3rd Floor of the Jubilife TV Station, you will find this couple. Normally he will ask you for a greeting for you to provide in battles however if you give him some keywords, he will activate the Mystery Gift function for you. The words are as follows:

Everyone Happy
Wi-Fi Connection

Now, on the main menu, Mystery Gift will appear and will sport just one option at first, two if you have received a Wonder Card. You will usually choose the only option which goes to another menu that has three options and an exit; Get From Friend, Get From Wireless & Get from Wi-Fi Connection.

Choose: Get From Wi-Fi
Get from Wi-Fi is exactly what it says on the tin. Using the DS's Wi-Fi Internet abilities, the game connects to the Internet servers and looks for any Wonder Cards that Nintendo has put up. The first use of this feature will be from September 28th to November 4th when Nintendo gives away the Secret Key to Obtain Rotom's Forms over Wi-Fi.
After you have received the gifts, you need to pick it up from the man in the PokéMarts. This gives you the actual item in-game and the delivery man can be found in any of the small PokéMarts within Sinnoh so you can get it anywhere. Once the Member's Card is picked up at the Pokémart, Save your game!

N+ Update: iMatio, dropped us a big update, this event if for Platinum owners only, sorry for the excitement Pearl and Diamond owners .

N+ Update2: It looks like this event does open the ferry up for travel, so now you can visit the New Moon Island and hatch pokemon there to have a sweet "hatched at" location.