Making local calls in Japan

I will be traveling in Japan for a month, I may have many local calls to make while outside and I don't to make use of my phone due to high roaming charge. I am told Japan don't sell sim card for a number. What can I do ?
Can a portable wi-fi make local calls ?
Will it be convenient to use public phones ?
Will public phones accept coins or do I need to buy any special card ?

Can a portable wi-fi make local calls ?

Yes, as soon you have n internet conenction, you can use Skype or similar software to call Japanese phone numbers.

Will it be convenient to use public phones ?

No, I would not call it convenient because they have become less common and have to be dealt with coins or phone cards.

Will public phones accept coins or do I need to buy any special card ?

I believe that most will accept coins and cards, but I have not used one in years, and my knowledge may not be up-to-date.

I am told Japan don't sell sim card for a number. What can I do ?

It is possible to rent sim cards, or get prepaid sim cards to use with your own unlocked phone. You could also rent a mobile phone.

Can a portable wi-fi make local calls ?

Yes, in conjunction with a smartphone/laptop and the proper software such as skype.

Will it be convenient to use public phones ?

Its not terribly, but your own mobile will be the most convenient of course.

Will public phones accept coins or do I need to buy any special card ?

Coins should be fine for local calls. Though if I recall correctly some require cards for international calls.