1. The 'cover story' must explain the event it's covering up well enough to endure all examination by media, law enforcement or other concerned parties.
2. Every conspirator must have a perfect understanding of the cover story. Discrepancies could lead to the truth coming out.
3. Every conspirator must have a means of contacting every other conspirator in complete privacy.
4. Every conspirator must be willing to go to any lengths to keep the secret, and must abandon any notion of gaining fame, wealth, legal indemnity, or other benefits by revealing the conspiracy.
5. Every piece of physical evidence must be destroyed, or placed in a secure location with incorruptible guardians. Forever.
6. Anyone who discovers evidence (and is not part of the conspiracy) must be blackmailed, bribed, killed, or discredited. Which, in every case, will require a cover-up of its own.
7. Anyone who might discover evidence must be monitored in some untraceable fashion for as long as they are a danger.
8. Members of the conspiracy must have access to the hardware, money, and other resources they will need to do all these things, and their access to such resources must be either secret or justified in the public eye.
9. No member of the conspiracy can be allowed to reveal it, so they must be in a position to silence any defector - yet each must trust the others not to misuse the power to kill or discredit them for any reason other than violation of the conspiracy.
10. Lastly, there must be some reason that they are failing to silence the Conspiracy Theorist.