It already exists:
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.The warrant could be issued for a particular place (say, the airport) and particularly describe the things to be seized (say, opiates).
AFAIK, customs searches have always been exempted from 4A.
If you think this is unconstitutional, you should have taken it up a couple of centuries ago with G. Washington, who set the precedent.
Here’s an interesting article on 4A and borders.
http://www.law2.byu.edu/jpl/papers/v19n2_Jon_Adams.pdf
The border exemption is based on the Constitutional power to “to regulate Commerce with foreign Nations. To do so requires prevention of smuggling and entry of unauthorized persons.