To cover-up extra terrestrial contact to the general public would require extensive cooperation between domestic agencies and international governments to maintain such a level of secrecy.
This type of secrecy is possible and can be illustrated by the SR-71 spy plane program. The general public found out about the project 30 years after it had been developed by Lockheed Martin Skunk Works. The SR-71 program required thousand of contractors and military personnel to develop and maintain the program yet there were no substantial leaks to the general public.
The secrecy was maintained by compartmentalizing the information on the secret project. Only a few key individuals had the complete picture of the covert program while the majority of the workers had limited amounts of information given to them on a 'need to know' basis. Individuals who were entrusted with classified information were carefully screened and tested before they attained the required security clearance needed to work on the project. Therefore, it is possible that information on contact with extra terrestrial beings could be compartmentalized; many people working on the project but only a handful knowing the whole story.
The following United States Intelligence agencies would have to cooperate with one another to maintain the extra terrestrials secret:
The previous list represents only the intelligence agencies in the United States. To maintain a cloak of global secrecy every intelligence agency around the world must cooperate with one another. Critics find it hard to believe that the governments of the world can cooperate to keep the biggest discovery of mankind secret while their own internal departments can't cooperate with one another.