http://www.paulding.gov/Facilities.aspx?Page=detail&RID=21
I think you have to rent the enclosed pavilion but the big picnic shelter at the top of the hill is first come, first serve.
My in-laws got married there last year and had to get over there at 7 am and sit at the gate to make sure they got the picnic shelter for the reception. But the number is at that link!