When John Gardiner invites U.S. senators to play tennis at his posh tennis ranch in Scottsdale, Ariz., he gets few refusals. In fact, he's even able to bring in members of the British Parliament. Gardiner holds a Senators' Cup tennis tournament each year to raise money for the Hospice of the Valley in Arizona and there are almost enough senatorial participants to reply to a quorum call.

About 25 members of the Senate have said they will compete in the 13th annual tournament this weekend. They include Gary Hart, Ernest F. Hollings, Dale Bumpers, Howard Metzenbaum, John Kerry, George Mitchell, Jake Garn, Paul Laxalt, Ted Stevens, Strom Thurmond, Malcolm Wallop, John Heinz, John Warner, Larry Pressler, Lloyd Bentsen and Dennis DeConcini.

Since this tournament features the United Kingdom Parliament versus the U.S. Senate, two members of the House of Lords and four from the House of Commons are traveling to Arizona to play. They are the Marquess of Reading, Lord William Kinnoull, William Cash, John Hannam, Jonathan Sayeed and Anthony Steen.

Other celebrity players expected: Swedish Ambassador Count Wilhelm and Countess Ulla Wachtmeister, entertainers Merv Griffin and Eva Gabor, "Peanuts" cartoonist Charles M. Schulz and FBI Director William Webster. Faulting Ferraro

There is general agreement that Geraldine Ferraro's autobiography, "Ferraro: My Story," was not a critical success, and it now has received a literary prize -- one she probably doesn't want. The American Spectator magazine has awarded her its ninth annual J. Gordon Coogler Award as the worst book of 1985.

In a review of the book in the January issue, New Republic senior editor Fred Barnes describes Ferraro's work as "a prolonged whine," and suggests the title should have been: "I'm Great -- It's Not My Fault I'm Not Vice President." He concludes that Ferraro "hasn't the foggiest idea why she and Walter Mondale were trounced." Other than that, it's a must for every political library. End Notes

World-renowned tenor Placido Domingo has been sidelined from his frenetic operatic and concert schedule for a pending operation. The Royal Opera announced yesterday that the singer has been told he must undergo immediate surgery in Barcelona for a double hernia. He will not be able to sing for at least two months, the announcement said . . .

Legendary folk singer Pete Seeger will be in town to join the Washington Philharmonic under the direction of Darrold Hunt for a special concert Jan. 19. The concert at the Metropolitan AME Church will celebrate America's first national observance of Martin Luther King Jr.'s birthday as a federal holiday . . .

Seeger, who has been involved in most major social movements of the past five decades, is also committed to perform in a 12-hour, antiapartheid benefit concert in Nashville April 12. Among the musicians approached to be part of that concert, sponsored by the South African Freedom Education Coalition, are Gil Scott-Heron, Holly Near, Stevie Wonder, Rosanne Cash and Little Steven Van Zandt. Van Zandt, a former member of Bruce Springsteen's E Street Band, was the driving force behind the antiapartheid album, "Sun City" . . .

After a six-month search, the League of Women Voters has hired a male executive director for the first time since its founding in 1920, and it's about time. The choice is Grant Thompson, a former senior associate at the Conservation Foundation; he previously worked at the Environmental Law Institute. The 120,000-member League has about 5,000 men on the rolls. League President Dorothy Riding said there was "no reaction at all" to hiring a man as executive director. And he won't be asked to type either. After all, he has degrees from Oxford and the Yale Law School . . .

Joe and Mo's bartender Matt Shean has also had it with Libyan leader Muammar Qaddafi. He is offering a Qaddafi Cocktail. As he describes it, "We don't know what the ingredients are, but they're disgusting" . . .