I searched the FAA website and cannot find the specific regulation, but it is made clear that replacement Airworthiness Certificates can be obtained for lost, damaged, illegible, or stolen (?) Airworthiness Certificates. It appears this process begins with a call to your local FSDO to request the correct form, and may involve a visit by a DAR to verify aircraft type, model, and serial number.
It is possible replacement information is available on the Airworthiness Certificate itself. Mine aren't handy at the moment.
