The days of scrounging for quarters amid the coffee-stained recesses of your car or sheepishly asking for change in stores while keeping an eye out for the parking officer could be nearing an end.

Mayor Thomas M. Menino will introduce a parking debit card today to give drivers another option at 7,200 Boston meters that until now were coin-only.

The officially named Boston Meter Card is designed to be swiped at the time of parking and again when leaving, so drivers pay only for time used, down to the nickel. That means no more racing back to fill an expiring meter or driving off with time left on the clock.

“We want to make it as convenient as possible for Boston residents and visitors to patronize our neighborhood business districts,’’ Menino said in a statement.

The prepaid cards can be purchased at City Hall and the city’s tow lot or online in increments from $5 to $100. Unlike the MBTA’s CharlieCard, the Boston Meter Card will not be reloadable from home, though officials said they hope to add that feature. Menino’s administration is also in talks with a major retailer to make the cards available in stores.

In interviews at meters yesterday afternoon, parkers were enthusiastic.

Roman Kubyshkovskyy, 30, who asked a passerby for change after parking his Volkswagen on Kingston Street, said it would end a perpetual coin search.

“It’s a good idea, because I don’t always have change,’’ said Kubyshkovskyy, who works in financial reporting. As a North End resident, stopping by City Hall is no inconvenience; he also liked the idea of using a prepaid card for a small amount. “That’s much better than debit or credit,’’ he said.

Some who park infrequently in the city said they would stick to coins, rather than obtain a special card.

“I don’t come into Boston enough,’’ said Ken Littman, 60, a lawyer from Jamestown, R.I., who snagged a spot on Chinatown’s Tyler Street. “If I came in every day and had to find a place to park - although I probably would go crazy if I had to do that - I probably would get it.’’

Amy Seto, 62, of Tewksbury said the ability to pay only for time used might make it worth it even though she visits Boston just twice a month. “That’s perfect,’’ said Seto, who works in the restaurant business. “Sometimes, I put $2 in, and if I leave in half an hour, I lose all the quarters.’’

Boston raised the parking rate from $1 to $1.25 an hour in January and collected $14.2 million from meters in fiscal 2011, which ended in June.