By most measures, Kathie Lee Gifford seemed to have it all: a glamorous job (co-hosting TV's Live with Regis and Kathie Lee), a loving husband (sportscaster and ex-football star Frank Gifford) and free vacations at sea (she's the spokesperson for Carnival Cruise Lines). But soon after Kathie's marriage to Frank in 1986, viewers of Live began pointing out the one thing that was missing from her charmed life: a baby. They begged her in letters, cajoled her from the studio audience. Once, recalls Frank, an elderly Italian woman passing him on the street shook her finger and asked, "When you give that lady bambino, bambino?" But Frank, 59, already father to two sons and a daughter (by his first wife), was reluctant to expand his brood, and Kathie, 36, didn't want to insist. "I was afraid it would spoil our love affair," she says. "I thought, 'Let's not rock the boat.' "

They didn't exactly rock the boat—they were on a 440-foot cruiser—but one evening last July, sailing off the coast of Italy courtesy of Carnival, the Giffords conceived Cody Newton, who weighed in at 8 lbs., 15 ozs., in March. "Our rhythm was a bit off," says Kathie, who admits she miscalculated her fertile phase by a week. "But when someone said, 'Is he a mistake?' I cringed. He's a lovely surprise."

And a big ratings boost for Mom's morning talk show too. When Cody was introduced to Live's audience, 41 percent of viewers in the show's home base of New York City tuned in—the syndicated program's highest NYC share ever. Even before the birth, ratings around the country had picked up as moms and about-to-be's followed each step of the pregnancy. With characteristic candor, Kathie chatted about everything from weight gain to tender nipples and complained that her belly button had transformed from an "innie" to an "outie."

Holding hands and nuzzling on the living room couch in their 1760 Greenwich, Conn., farmhouse, the Giffords ooze parental bliss. Kathie calls Frank "Diddy" (that's "Daddy" in Shirley Temple-speak, she explains), and they both coo over their son, calling him "Codesville," or "Mr. Mad" when he cries. Obviously smitten by his latest shot at parenthood, Dad says, "The most wonderful thing you can share is a baby."

Kathie, a Maryland native and a born-again Christian at 12, was a nightclub singer and actress during her seven-year marriage to gospel composer Paul Johnson. The union was unraveling in 1982 when she occasionally co-hosted ABC's Good Morning America with Frank—who was himself having marital problems with his second wife, Astrid. They quickly became pals, but the friendship, they insist, remained platonic. From time to time, in fact, Frank fixed Kathie up with his bachelor buddies. "He seemed so uninterested in me," she says. "I thought, 'What a wonderful guy,' but a serious relationship really never dawned on me."

But in July 1986—a year after Kathie joined Regis Philbin on Live—love suddenly blossomed. At a friend's party one night, Kathie and Frank (who had been separated from Astrid for two years) broke into a silly rendition of "You Don't Bring Me Flowers." According to Kathie, Frank sang with "no rhythm, no tone, nothing. I fell off the sofa laughing. I looked at him and thought, 'I don't want to live without that man.' It's a wonderful thing to fall in love with your best friend." A month later—Frank's divorce had come through—the couple pledged their passion over a five-carat diamond.

Cody has forced certain changes in the couple's previous wine-and-candle-light life-style. They've hired a nanny and a live-in couple to cook and keep order. In preparation for nocturnal visits to his son in the more crowded household, a modest Frank, who used to sleep in the buff, now wears a sweatsuit to bed.

Teasingly, Frank tells Kathie that the baby looks exactly like him. "We have the same profile," he observes. "Except Frank's nose has been broken four times," Kathie rejoins, adding, "We want Cody to play gentleman sports—no boxing, no football, no hockey. As his mother, I'd like to protect his face."

Well, then, how about opting for Mom's career instead? Of course, it will be tough to top the hype surrounding Cody's TV debut. "Now that he's had a 41 share, he's very arrogant," notes Frank. "Has his agent called?"

—Jeannie Park, Maria Eftimiades in Greenwich, Conn.