Denver might become the babysitting capital of the United States, thanks to Jim Kone.

Kone, the co-owner of a steel service center, sold his interest in the $14-million business to found Rent-A-Mom, a company that provides professional child care to Denver residents and visitors.

After a Denver bank "quit laughing at the name of the company, it told me to come back in two years," says Kone. Instead of waiting, he invested $10,000 of his own money and opened shop in August 1981. Sales for 1982 are projected at $250,000.

Kone originally planned to provide qualified, insured child-care workers to major hotels in Denver, but he soon expanded his service to offer live-in nannies, traveling nannies, tutors, pet and house sitters, and city tours for children. He has sent one nanny to Switzerland, and filled another family's request for a French-speaking woman over 50.

The hardest part of the business, says Kone, is coordinating personalities -- he usually sends three nannies to a home before one works out. Kone, who is just as choosy as his customers, interviews between 15 and 20 people a day and rejects 60% of then.

Kone's staff includes five office workers, a manager, and more than 200 nannies who range in age from 22 to 75. The majority of Rent-A-Mom's customers are middle- to high-income working couples who pay between $5 and $6 an hour for residential and hotel sitting. "Our business serves as an extension of the working family," says Kone, whose biggest demand is for sitters to "greet the kids home from school, entertain them, cook them dinner, and then go home."

These days, Kone has no problems finding a sitter for his two children, and he thinks the service is "great." His opinion is biased, however: "I always get the cream of the crop," the 40-year-old entrepreneur admits.