OK, there are many ways to find Darkrai but here are a few examples...
1. Go to Canalave City (in Platinum. just for an example) and go to the Radio Tower and get the Member Pass (is not available anymore until near future.) and take the member pass and go into the house with the door that normally won't open. There will be a guy in there and a bed and he will say, "character's name,we have had a reservation for you for a long time. Please go to sleep." and when your character does, you will end up on New Moon Island. Walk into a woodsy area and you will see it. Since it is a legendary, I recommend saving while on the island because there is only one of it and if you defeat it, your screwed.
2. You can also get it in an event in the near future
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you need an action replay with the code that allows you to reun thru everything. go to full moon island,start runnig directly to the right in the ocean. keep going until you reach an island called new island. that's were youl find darkrai.
Have fun catching Darkrai! Use a ActionReplay and look for walk or run anywhere through anything at the bottom travel to fullmoon island than go walk on the water to new moon island to get darkri
You need to go to a special past event and get a membership card then go to the inn in canalave city you will have nighmares then wake up on an island called fullmoon island there you will find darkrai
He can be found at Miracle Sea at floor 3. You have to have a mystery part or secret slab for him to appear. In case you don't have one, here's the wondermail for it.
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Please note despite him being a dark type, he can go through walls like ghost type Pokemon, so don't be surprised if he's inside the walls. It is recommended that you go with one Pokemon so you don't have to worry about partners killing him.
You can't find Darkrai in Pokemon rumble, you have to go to the releasing house (blue roof) and release:Wash Rotom, Heat Rotom, Spin Rotom, Cut Rotom, Frost Rotom after you release then a darkrai ticket should come out, collect it then head over to the recruitment house (red roof) and select recruit with ticket and there you have it a darkrai!
If you don't know how to get the rotoms then you have to release:Rotom, Glaceon - Frost Rotom.Rotom, Leafeon - Cut Rotom.Rotom, Flareon - Heat Rotom.Rotom, Jolteon- Spin Rotom.Rotom, Vaporeon - Wash Rotom.
Darkrai is currently not obtainable in Pokémon X and Y.
However, you may transfer one from Pokémon Black, White, Black 2 and White 2 once the Pokémon Bank and Poké Transporter apps are released in December 27th, 2013.
You can only find Darkrai through a Pokemon Event.
in map 10
Maps 25-26
I found a bunch in the Pokemon Tower, Map 24.
You can find Rayquaza in map 13.