Reserving area off Shore road in Bay Ridge

Does anyone know who to contact if I want to reserve an area off Shore road for a kids party. I know there are no tables or BBQ's anywhere in those areas down off the road but Id like to maybe do a picnic and have games. Even rent a moon bounce or Jumper (I don't know the correct name).
I want to reserve an area down off the road by where the baseball fields and playground is near 95th and shore. Im not sure how to explain this.

Or
If anyone has any ideas where I can pull something off like this. I need to plan my sons 4th bday party for the 27th or 28th of this month.

Thanks for suggestions and help.

Samantha