When Gary Mandarino got an urgent order for a refurbished 30-year-old carousel—4 feet in diameter and 7 feet tall—the befuddled owner of Denver-based Kiddie Rides didn’t know whom it was for. But he did have a zip code: 90210.

The Colorado company focuses on restoring nostalgic 20- to 40-year-old coin-operated children’s rides. Normally, the rides take two to four weeks to overhaul, but for the 90210 mystery customer, he only had a week. The customer, his shipping company informed him, was the actor Michael Caine, who reportedly wanted it for the birth of a grandchild. The top-priority transaction cost $6,000, plus more than $1,200 in overnight shipping charges. It was the fastest turnaround Kiddie Rides has ever pulled off.

James Otto Hahs of Missouri, the inventor of the kiddie ride, probably never would have imagined that his 1930 invention—a mechanical horse that was originally conceived as a Christmas present for his children—would see a comeback for today’s well-heeled child. Mandarino says there are no manufacturers of kiddie rides left in the United States, so when somebody wants one to see one come to life again, they come to him. But the luxury of reversing time has a hefty price tag. Refurbishment of the rides can cost between $2,600 to $9,000.

In early December, the holidays had Mandarino rushing to get six rides out the door within two weeks. “I’m not in a panic mode,” he says, “but a lot of people call and think there’s something sitting on the shelf and ready to go.” On the contrary, Kiddie Rides only does custom orders—such as putting a child’s name on a ride or matching it to a room’s décor—so it can have “that personal, individualized touch.”

“I’ll get calls around Christmas where people say, ‘I need one tomorrow,’” Mandarino says. “That just can’t happen—but usually I’ll persuade them to order one anyway.”

After working for the business for five years, co-owner Mandarino, 60, purchased Kiddie Rides from his former boss in January 2014. Mandarino worked for years in the special effects industry and moved to Colorado from Pittsburgh in 2005. He handles the mechanical and electrical side, and his painter, Brandon Hovet of Brighton, decorates the rides with auto-body paint. Hovet once spent a month stripping 15 to 20 coats of paint off an old stagecoach ride for a farm in California, then Mandarino took an additional month to rebuild the body and all its mechanics. (Mandarino estimates only 10 percent of the rides he takes into his shop are functional.) Most of the rides come from individuals who’ve had one sitting in a basement or garage for years, but Mandarino also has “regulars”: Three collectors in three different U.S. cities, he says, “who have warehouses full of these rides.”

Kiddie Rides ships its goods all over the country and the world, but selling a pair of vintage horses to the Denver Zoo is the only Colorado business Mandarino has done. All his sales are Internet-based or over the telephone, and he doesn’t spend a penny on advertising. “I don’t have any walk-in customers,” he says. “These are not impulse items.”

Mandarino enjoys the challenge of getting the beat-up rides up and running again, and has a major soft spot for the way they evoke more innocent days. “We take this very seriously,” he says. “We are reviving pieces of American nostalgia. Life was so much simpler back then, and we feel good about keeping this alive.”

(Read more: Six Ways to Have Vintage Yuletide Fun)