Can I discard clues from the Cover Up card when at a location with no clues?
No, you definitely can't use it at a location that has no clues on it.

The triggering condition for this reaction is 


  When you would discover 1 or more clues at your location: ...


And the rules reference (on page 7 under Clues) states


  A card ability that refers to clues “at a location” is referring to
  the undiscovered clues that are currently on that location.


This means that you must first have the possibility of discovering at least one clue at your location, and then be the target of a game effect (investigating the location, an Event card, or some other means) that instructs you to discover at least one clue at your location.

The triggered effect also specifies that this would not be of any use to you on a location with zero clues. It says


  ... Discard that many clues from Cover Up instead


Even if there was no minimum limit of discovering 1 clue at your location, discovering zero clues at your location would result in zero clues removed from Cover Up.

Also note that Cover Up, like all Triggered abilities controlled by the player, is optional to perform. So you can opt to discover the clues if you feel it is of the most benefit to you, or you can opt to discard the same number of clues from Cover Up instead.