Sleep from Darkrai can be very annoying, and it has stopped me a few times as well, but here are a few strategies.
Taunt
If you manage to taunt Darkrai, it won't be able to put you to sleep anymore. Taunt is also helpful in a bunch of other battling situations, such as stopping them from setting up field hazards, so that helps you even more. Here you can find out who can learn this move.
Vital Spirit/Insomnia
Pokemon with these abilities cannot sleep at all, so they would be able to continue attacking without falling victim to Dark Void. Darkrai's whole annoying part would be useless, and this is a great way to stop them. Check here and here to find out which pokémon can have this ability.
Clerics
A Cleric is a pokémon who uses the moves Heal Bell/Aromatherapy to heal everyone from status conditions. It can be tricky to pull off and there are ways your opponent can break this strategy (like putting your cleric to sleep) but I thought it was worth mentioning. IMO Eviolite Chansey is a good cleric that has worked well for me, but try different things and pick whatever you find easy to use.
Getting another status condition
Yes, this can seem like a bad idea to some people at first. Why put a status on yourself? What good will it do? Well, pokémon with the ability Guts or Toxic Boost or Poison Heal with a Flame or Toxic Orb can benefit from this. You can only have one status at once, so if you already are poisoned or burned, they can't put you to sleep. Here for Pokemon with Guts, here for those with Poison Heal. Only Zangoose can have Toxic Boost.
Substitute
You cannot be put to sleep while behind a substitute (not saying you cannot be asleep behind a substitute), so you can quickly set one up before they get to use Dark Void. Substitute can also allow you to set up field hazards and burn/paralyze/poison/put to sleep/confuse/other the opposing Darkrai. Many different Pokemon can learn this move.
Just defeating them before they have a chance
Sometimes, you can just grab a fast Pokemon and quickly sweep Darkrai if you don't have any Pokemon who can do any of the tips I've listed (which is unlikely) or you just want to get rid of that thing right away. It's weak to fighting, bug and fairy moves, so pick strong moves of that type, with accuracy in mind.
You'll also want to have speedy pokémon for most of these tips. Darkrai's base speed is 125, so you'll need something that can outrun it and dish out good hits, if you decide to sweep.
Hopefully these tips will help you defeat that annoying Darkrai :D!
Sources: A question my friend asked and also some other tips from my own experience.
