Search for special promotions that are open to new AMEX applicants. AMEX periodically has offers waiving the annual fee for a new member's first year. Look for AMEX platinum card offers on the Internet, or talk to AMEX representatives at airports who are taking applications in person.
Check for offers that are available only to existing members. AMEX platinum card applications sent with statements offer no annual fees. Also, customers receiving e-statements can access offers online waiving the annual fee on an AMEX platinum card if a specific amount of money is spent in a billing cycle.
Call AMEX member services and ask about applying for the AMEX platinum card. When the representative mentions the annual fee, find out if they would be willing to waive the fee for the first year. The representative can sometimes find a supervisor willing to approve the request.