The Dallas Cowboys may have been whipped, 44-0, by the Chicago Bears, trounced, 50-24, by the Cincinnati Bengals and shut out in the NFL playoffs by the Los Angeles Rams last year, but they remain favorites of the television networks.

According to the National Football League schedule released yesterday, the Cowboys will have the maximum three appearances on ABC television's "Monday Night Football" this fall, although one of the games will actually be played Sunday night.

For the fifth season in a row, the Cowboys will open the ABC football series. This year, it will be a home game Sept. 8 against the New York Giants; last year it was against the Washington Redskins.

They also will have a Monday night game against the St. Louis Cardinals and a Sunday night contest against the Los Angeles Rams, who beat the Cowboys, 24-0, in the playoffs.

The Cowboys will follow the Giants game with contests against the Detroit Lions and Atlanta Falcons and will then go to St. Louis for the Monday night meeting with the Cardinals, who are coached by Gene Stallings, one of five former Dallas assistants who is now a head coach in the NFL.

The Cowboys will face a tough 10-game stretch after that, including matches against Denver, Washington, Philadelphia and the Los Angeles Raiders. They'll close out the regular season with consecutive home games against Philadelphia and the Bears.

In other news out of Dallas, the Cowboys promoted reserve quarterback Steve Pelluer to the No. 2 spot behind Danny White because backup quarterback Gary Hogeboom wants to be traded . . .

Atlanta Falcons Coach Dan Henning announced the team has obtained quarterback Turk Schonert from the Cincinnati Bengals in exchange for a third-round choice in the April 29 draft.

The trade with Cincinnati is contingent upon the 29-year-old Schonert passing a physical examination. He also must sign a contract with the Bengals, which then will be forwarded to the Falcons.

Henning also said the Falcons, who will choose second in the draft, plan to take Oklahoma nose tackle Tony Casillas. Tampa Bay, which has the first choice, has indicated it will take Heisman Trophy-winning running back Bo Jackson of Auburn . . .

The management of the Portland Breakers, unable to find local investors for the U.S. Football League franchise, plans to sell the team's equipment to pay a $50,000 tax bill.

Lou Ellen Pearson of the Oregon Department of Revenue said the team owes the state $46,925. The Breakers owe Multnomah County another $2,785. BASKETBALL

Quintin Dailey of the Chicago Bulls has requested and been granted a leave of absence for the remainder of the season because of a drug problem. Dailey relayed the request through Gary Bettman, head of the NBA's drug program, and Jerry Krause, vice president of operations for the Bulls, said the team would comply with the request.

Last October, Dailey admitted he had a drug problem and entered a rehabilitation center in California. It was his first offense under the NBA's drug regulations. He was released 31 days later and rejoined the team. On Feb. 5, after skipping a game in Detroit, he again admitted to drug abuse and asked to reenter a rehabilitation center. COLLEGES

Patrick Knapp was named women's basketball coach at Georgetown, succeeding Cheryl Thompson, who resigned in March. Knapp moves to Georgetown from New Mexico State, where he compiled a 45-39 mark in three years, including a 20-8 season this year. Knapp is a 1975 graduate of Widener College, where he guided the Pioneers to two appearances in the NCAA tournament . . .

Darlene Beale of Howard was named an all-America and women's basketball player of the year by the Black College Sports Information Directors Association. Other first-team all-Americas were: LeChandra LeDay and Mary Currie of Grambling State, Patricia Walker of Prairie View A&M and Rose Willis of Morgan State.

Jackie McKinnon of UDC was named to the freshman all-America team and teammate Tracey Walton was named a third-team all-America. TENNIS

Unseeded Mikael Pernfors returned to Georgia in fine fashion, upsetting No. 1-seeded Stefan Edberg, 7-5, 5-7, 6-2, in the third round of the $279,000 WCT-Atlanta tournament. In a night match, second-seeded Boris Becker, the West German star currently ranked fifth in the world, was also upset, losing, 6-2, 2-6, 6-1, to Tim Wilkison.

Pernfors, a Swede who was last year's NCAA singles champion, played at the University of Gaorgia, winning his title on the school's Athens campus, about 60 miles from Atlanta . . .

Jimmy Connors, just starting a 10-week suspension, will be able to play in the Beckenham tournament, a June 2-8 tuneup for Wimbledon, tournament organizers said.

Connors, ranked fourth in the world, was suspended for 10 weeks and fined $20,000 for defaulting in a semifinal match against Ivan Lendl in the Lipton International Players Championships in Boca Raton, Fla., in February.

The suspension will end June 8, which is the last day of the French Open as well as the Beckenham event. Connors' suspension bars him from playing in the French Open, but not at Beckenham . . .

Ivan Lendl will definitely miss the next two weeks because of tendinitis in his right knee, his agent, Jerry Solomon, said. Solomon said if the problem persists Lendl will have further exams next week to reveal whether there is a tear in the tendon. RUNNING

The Boston Athletic Association announced the Boston Marathon's new finish line will be located between the old and new sections of the Boston Public Library on Boylston Street.

Runners in this year's marathon will finish near the corner of Boylston and Dartmouth streets near the 60-story John Hancock Tower, the corporate headquarters of the John Hancock Financial Services, the marathon's new corporate sponsor.

As an added attraction, a 30-foot-wide high-resolution color television screen will provide video coverage of the race to thousands of spectators in Copley Square.

"The new location is going to make for a much more scenic and enjoyable finish overall," said BAA spokesman Guy Morse, noting the finish line has been moved about 300 yards down Boylston Street from its previous location at the Prudential Center. LOCALLY

A benefit basketball game between the WMAL "Radio Oneders" and the Kennedy High School faculty will be played April 10 in memory of Brady Straub, the Kennedy football coach who died of cancer in February. Tickets for the 7:30 p.m. game at Kennedy will be available at the door.