Did you see that prop guy walking down 5th Avenue with the two rubber aliens? They must be filming in the city. *yawn*
Fine. Call a reputable local paper, and get someone reputable to walk down with you to the City Coroner. Dump these two bodies on the steps of the building the coroner is on. You'd have cameras there live within 5 minutes. Coroners could tell the difference between a rubber dummy and a real body. You'd have a live feed going all over the city before the MIB would have anything close to a wiff of it.
In the information age, suppressing something like that is impossible. Too easy to prearrange for multiple visual witnesses and media coverage that could not be silenced in time. Heck, cut off bits of the thing before you turn it over, and send them to research labs around the country to be analyzed. When they see the DNA or whatever its got, the lid is blown. Impossible to suppress. Keep a bit or two for yourself, give TV interviews, etc. No way to silence that. No way.