Sure, it's exactly like implementing GET,

In your subclass of Apache2::REST::Handler, just implement DELETE or PUT:

 sub PUT{
   my ( $self , $req , $resp ) = @_;
   .. Do put something in this resource ..
   .. Fill resp if necessary ..
   .. Return the appropriate http code
   if( $somethingWentWrong ){
     return Apache2::Const::HTTP_BAD_REQUEST ;
   }
   # else it's ok
   return Apache2::Const::HTTP_OK ;

 }
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