What is the best way to get more men to take paternity leave?

In Japan? The only way would be to fine men who don't take it. Say, fine them a month's salary. Even then, the take-up rate wouldn't be 100%.

Just say that the company has an obligation to BUY those paternity days. Say 100,000 yen a day must be paid to the employee for everyday they do not take.  That should ALSO be extended to the regular paid holidays that go untaken every year. The company must BUY them from the employee. Then watch the company Shacho scream at everyone to take time off so that the company doesn't go bankrupt. Simple

Mind change from boss and colleagues for some understanding ?

Not going to happen since solidarity is blatantly absent and bachelorship is widespread.

IS there even paternity leave in Japan? Like proper leave covered by the social security/national health scheme?

To make it available for starters.

Second, to publicize its availability.

Aly RustomSep. 26  10:23 am JST

Just say that the company has an obligation to BUY those paternity days. Say 100,000 yen a day must be paid to the employee for everyday they do not take. That should ALSO be extended to the regular paid holidays that go untaken every year. The company must BUY them from the employee. Then watch the company Shacho scream at everyone to take time off so that the company doesn't go bankrupt. Simple

For most places I've worked at, this is a sure-fire way to get every staff member to demand their paternity leave be bought. Hell, I'm fairly ruthless about getting out of work whenever possible and I'd consider giving up my paternity leave for that kind of money. I'd expect a lot of Japanese wives to be okay with it. They're already used to their husbands not getting paternity leave, only now they would get a substantial cash bonus out of it.

inkochiSep. 26  02:07 pm JST

To make it available for starters.

Second, to publicize its availability.

Pretty much this, but managers should be a little pro-active about pushing people to take it. It may be hard to get the ball rolling because people don't actually have children that often here, but once it becomes a consistent habit, it will feel "normal".

Employers should encourage it . . . if fathers wish to have a healthy child, then be prepared to help out with family at home.

Actively offer it and assume it will be accepted - make it a default part of every employee's contract.