Airline Competition Enhancement Act of 1989 - Amends the Federal Aviation Act of 1958 to require the Secretary of Transportation to ensure that computer reservation systems are available to all air carriers, ticket agents, and other persons on a nondiscriminatory basis. Prohibits air carriers (or affiliates) from operating such a system after January 20, 1991.

Prohibits such a carrier from: (1) sharing its designator code with another air carrier for computer reservation purposes; and (2) using the designator code of another to identify a flight.

Amends the Federal Trade Commission Act to provide that domestic and foreign air carriers shall not be under the jurisdiction of the Federal Trade Commission with respect to enforcement against the use of unfair methods of competition or deceptive practices by such carriers in the industry.

Amends the Federal Aviation Act of 1958 to declare that an air carrier operating aircraft at a concentrated hub airport shall be presumed to have been engaged in unfair or deceptive practices or unfair methods of competition in air transportation (or the sale thereof) if such carrier is a dominant air carrier at such airport.

Authorizes the Secretary to seek injunctive relief in district court against domestic and foreign air carriers, or ticket agents, who have been or are engaged in unfair or deceptive practices or unfair methods of competition in air transportation.

Authorizes the operator of a concentrated hub airport to assess a charge on passengers enplaning at such airport.

Directs the Secretary to implement a rule that provides for the withdrawal and transfer, by auction, of slots held by domestic and foreign air carriers at high density traffic airports. Requires deposit of the proceeds from any auction in the Airport and Airway Trust Fund for use in projects to enhance airport capacity.