Starting Wednesday, each passenger flying on an Eastern Airline Air-Shuttle flight this month will be given a bonus coupon good for a 50 percent discount on a one-way coach or first-class ticket on Eastern's flights between New York and California, Eastern announced yesterday.

The coupons will be valid for travel from Jan. 12 through June 10 and will apply only to the regular one-way adult day coach, night coach or first-class fare on Easterns transcontinental flights, and not to special or discounted fares. The plan is subject to almost certain Civil Aeronautics Board approval.

The coupons will be passed out to all passengers, including children, on Eastern's shuttle flights between Washington and New York, and New York and Boston, except on flights between noon Saturday and noon Sunday when Eastern dropped its fare from the regular $59 to $29 to match the weekend fare of New York Air.

Under the plan, a passenger with a pair of coupons would spend $569 instead of $1,038 for a round-trip first-class ticket between New York and California, $438 instead of $876 for a round-trip day coach or first-class night ticket and $350 instead of $700 for a round-trip night coach ticket.

Although Eastern offers lower Super Saver fares on its transcontinental flights, they are limited and carry with them advance-reservation and -purchase and minimum- and maximum-stay requirements. The discount fares cannot be used easily by business executives who generally do not make reservations two weeks ahead of a flight and often do not stay a full week, as required.

The Eastern coupon program is designed specifically for business people; they represent the bulk of the shuttle market and could view the coupon as an inducement to fly the shuttle rather than New York Air's new lower-fare service between Washington and New York. In addition, Eastern officials hope the coupons boost travel on Eastern's 10 daily round-trip flights between New York and California.

Just a few hours after Eastern's announcement, one of its chief competitors, Trans World Airlines, said it would honor any of Eastern's half-fare coupons for use on TWA flights between New York and Los Angeles or San Francisco.