Anyone willing to pack up and move to the remote southern village of 379 residents would get a no-cost calf or 500,000 yen ($4,900) in cash.
Mishima's bovine brainwave has fallen well short of expectations, however.
"The programme has been going for more than 20 years, and so far there has only been one person who took us up on the cow, and that was two decades ago," village official Shingo Hidaka told AFP, adding the cash had only a handful of takers.
The town's plucky bid to reverse its demographic drain may be unusual, but it is not alone.
In an effort to lure newcomers, small communities across Japan are offering new arrivals everything from sacks of rice and school lunches to no-cost medical care and free entry at the local hot spring -- a hugely popular pastime.
But the mostly ineffective moves have proved no match for the twin threats of a rapidly ageing population and one of the world's lowest birthrates.
As a result, Japan's countryside is emptying out at an alarming rate, in a demographic shift that by government estimates will see the population drop to 86 million over the next four decades from about 127 million now.
A whopping 40 percent of the population is expected to be over the age of 65 in the coming decades, up from around a quarter now.
The problem has left some communities overwhelmingly populated by elderly people or on the brink of becoming ghost towns.
School rolls are badly diminished and local services are increasingly too costly to maintain due the shrinking tax base, while the problem hurts the wider economy and exacerbates an already severe public debt crisis.
The privately-run Japan Policy Council warns that by 2040 about half of Japan's communities -- from the biggest cities to tiny hamlets -- are at risk of tipping into an irreversible decline, mainly due to sharp drop in the number of young women in remote areas.
But it is not only an issue for the countryside, as overpopulated cities suffer from worsening social services, warned Hiroya Masuda, a former internal affairs minister and the policy council's chair.
The exodus has seen younger people flock to bigger cities, including Osaka and the capital Tokyo, whose metropolitan area is home to about 30 million people, or nearly one-quarter of the nation's population.
"The country is going to lose its balance if Tokyo is overcrowded and there is no one in the countryside," Masuda said.
"We have to look at this issue as today's problem."
Case in point is Nanmoku village, 100 kilometres (62 miles) northwest of Tokyo, home to the country's oldest population.
A record 57 percent of its residents are 65 or older, and the government estimates that there will be just 700 people living in Nanmoku by 2040, plummeting from just over 2,200 now.
The village is offering free school lunches and student medical care to anyone willing to move to the area.
Hida in central Japan is giving newcomers an annual gift of 60 kilogrammes (132 pounds) of rice for a decade, while Nikaho in the north will hand out free admission to the local hot spring.
"But the situation has been getting worse and worse -- we haven't found the kind of radical steps needed to stop the trend," a Nanmoku official said.
The once bustling whaling town of Ayukawa is now a shell of its former self after a ban on commercial whaling decimated the economy, with the population plummeting by 75 percent since its peak in the mid-1950s.
"Those were the good old days," said Kinji Suzuki, a 77-year-old retired whaler, as he stood on the town wharf with a whale-tooth necklace dangling from his neck.
"Without whaling, people will leave and this town will die out."
Prime Minister Shinzo Abe has pledged to unveil an action plan by the end of this year to halt the decline and stabilise Japan's population at around 100 million.
Abe last week shuffled his cabinet, creating a new ministerial job dedicated to revitalising local economies.
"Our government is feeling a sense of crisis about this lack of a vibrant countryside," Chief Cabinet Secretary Yoshihide Suga, the government's top spokesman, said recently.
"Building strong communities in rural areas is a crucial job for us."
Hideo Kumano, chief economist at Dai-ichi Life Research Institute, warned against anything that hints of Japan's notorious pork-barrelling ways.
Big government projects aimed more at winning votes than economic growth would only inflate one of the world's heaviest public debt burdens, Kumano said.
"The era of excessive spending on random public works projects is over," he said.
Reconstruction projects in communities devastated by Japan's 2011 quake-tsunami disaster have supplied jobs.
But some fear that it is just a temporary fix and will do little to keep the dwindling number of young people from moving away from towns like Otsuchi, which was devastated by the natural disasters.
"If my children decide they want to leave when they get older, I don't think I could find a reason to stop them," said resident Manami Suzuki.
"I can't imagine what this town will be like in 30 years," said Suzuki.