Rental car in Ishigaki

Hello, I am visiting Ishigaki Island for 5 days during June with my family. I have an Indian driving license. Though I don't have any international DL, I would like to know if there is any possibility to get a car on rent for a day.
Is it possible for any hostel to provide us with a car? I'm curious to know how foreigners deal with this in Japan.
Additionally, I am aware that Ishigaki do not have much bus frequency which could be hard for any foreigner to travel around.
Any kind of suggestion will be appreciated.

I have an Indian driving license. Though I don't have any international DL, I would like to know if there is any possibility to get a car on rent for a day.

You cannot drive without an international DL. But I think that the international DL issued in India are recognized by Japan. The basics are here:
http://www.japan-guide.com/e/e2024.html

Is it possible for any hostel to provide us with a car?

In Japan it is usual for tourists to rent a car through a car rental company. But some hostels may be willing to help make you a reservations. I would not count onto it, though.

I'm curious to know how foreigners deal with this in Japan.

They get an international driving licence in their home country and then make a reservation for a rental car through a rental car company. There are more and more rental car companies that accept reservations in English. See the linked page above for details and links.