In designing a cooperative game I've been aiming to come to an understanding about what people want from the genre. Two things have really stood out for me; the first is that people who play cooperative games seem to really like losing. In discussions on the subject most people like games where they lose 70% of games and few people get seriously upset at the difficulty until that hits 95%. There's some variation here and a few people like games that they win more than half of the time, so I'm interested in variable difficulty (a topic for another day) but from the conversations I've had and have observed I should expect people to set the variable difficulty to "hard".
The second thing is that people hate losing for reasons beyond their control. When they lose they want to think "We could have anticipated that threat and done this thing" or "If only I knew my left from my right", in short they want to see how they might have won. When I got negative feedback about the difficulty in Wizard Academy in the first playtest it more often took the form of "And then the game prevented us from doing anything" rather than "And then we did the wrong thing". Perversely since I made big fires spread faster I've had fewer complaints about difficulty, since it means that a big fire hits for damage sooner and doesn't trap the players in place for ages. So they're always doing something which in turn makes it feel like their failures come from doing the wrong thing rather than from arbitrary difficulty.
I think that the best cooperative games out there are made successful by the tricks that they use to make their players make mistakes. If you want your players to lose a lot of games that are winnable then you need to get them to do the wrong thing sometimes, but players tend towards being clever so the games have to trick them. I'd put them into three categories:
Rewarding Bad Behaviour
If a game makes suboptimal play feel rewarding in the short term, then that'll lead players towards mistakes. I think Arkham Horror is a great example of this; two of the most successful strategies are having someone sit on the curiosity shop spending all of their turns looking for elder signs and having everyone tool up for the final fight and not to try to stop the thing waking up. These are both boring. The interesting things tend to be less strategically good options, so players are lead towards them and only have themselves to blame when it all goes wrong. Personally, I don't like this approach, I think that winning and having fun should go together wherever possible.
Blaming Players for Random Events
A successful strategy can be derailed if the group is surprised by an element of the game doing the wrong thing at the wrong moment. The trick here is to make it feel like whatever the game is doing is somehow the players fault, or something they should have mitigated. Pandemic does this brilliantly. The players know that when there are three cubes on a space that they really should do something about that. When such a space gets an extra cube and explodes, due to a draw from a random deck, the players almost always blame themselves for having prioritised something else over cleaning up that space. They also know how many epidemics are in the deck and develop a fair sense of when one is "due" so when an epidemic makes everything awful forever they don't think "Stupid random card draw ruining everything" they think "Stupid us, not properly being ready for the epidemic we all knew was coming.".
Increasing the Cognitive Load
Some games can achieve difficulty without an arbitrary nature by adding discrete stresses to the human brain to the point that it is no longer able to plan effectively. Going back to my psychologist roots briefly, having people do one task makes them worse at other tasks, you can adversely affect someone's reaction time by making them count backwards while performing the other test. There are volumes written on what sort of tasks interfere with what other sort of tasks, but from a game design point of view the essence of this solution is to load the players up with conflicting tasks until they make mistakes all on their own.
My favouriate cooperative game, Space Alert, does this very well. Players are operating on a time limit. Players are periodically getting new information. Players need to parse information they receive and make sure they filter the key information to other players. Players need to listen to the tape and do what it says when it says it. Players need to coordinate with each other. Players need to remember to have someone wiggle the mouse. Players need to remember the predicted board state at different turns and be aware that the pieces on the board may not match that. Players need to know their left from their right. The most common cause of death in that game is someone not knowing left from right, it always feels like your fault when you do it and everyone does it at least once. It's not that people can't tell their left from their right, it's that they get overloaded by the game and can't think under pressure. This doesn't always require a time pressure; it can be achieved by making a game of sufficient depth that the consideration of every consequence of a move is a challenging task in its own right.
There are more approaches than these, but these are the three that leap out at me as the most common. I've heard good things about Space Cadets, for instance, which uses dexterity mechanics to make it possible for a player to make a physical mistake. I don't really know much else about the game though, I should get a copy at some point. Personally I'm going to ignore 'rewarding bad behaviour', dip into 'blaming players for randomness' and focus on 'increasing cognitive load'. You can take the psychologist out of the university, but you can't stop him looking for ways to remotely mess with the heads of everyone he ever meets.