I think monkeys get too emotional for full cooperation all the time, but in short interavals you could probably do it.
monkeys were trained for the earliest american space flights. they had to fire the retrorockets to reenter the earths atmosphere. i think that qualifies as "cooperation".
they're pack-animals if i remember right, not unlike dogs, and as such, cooperate naturally like spidergoat said. why else do you think man and dog get along so well?
Oniw, well, let's discuss how it can be done. I think, if you can get the monkeys to associate certain objects with reward, like giving the monkey a certain signal, and physical object of a certain shape to mean reward, you can convince the monkey to want that object, and thus do what you want to get that object, which if collected, will equal rewards. But you can only give that objects to monkeys who cooperate.
Baboons even cooperate with gazelle. Although they do occassionally sneakily betray gazelle and eat their young, they at least have the decency to be discreet about it and they're clearly ashamed when caught in the act.
As several posts have noted, most monkeys are pack-social animals and have an instinct to cooperate for their own welfare and that of the pack. As was also noted, dogs have this instinct too. Yet some breeds of dogs are much better at bothering to learn and perform complicated activities than others. Poodles and Maltese live for performing tricks, whereas my Lhasa Apsos... let's just say you'll never see one even entered in an obedience trial, much less winning. We've domestically bred certain bloodlines of dogs that have a stronger cooperative instinct. We'd probably have to do the same thing with monkeys.
Trained monkey can even make a timetravel back to Ronald Reagan Trained monkeys can do a time travel. ( seen in the "Planet of Apes" remake ) So monkeys with a letter from the President, and some video tapes as proofs, could be sent back to president Ronald Reagan in office 1980-88, to inform him about coming political world evolution, and tell him what to do and what not to do. I think Ronald would not consider these as fakes, because vice president George Bush would identify his son on the videos as authentic. The advantage of sending monkeys, not people, would be that they cannot talk and reveal things they should not reveal in the past, if arrested and questionned.