When I looked up the phone number you can go on the website and look up the phone number to JB Sparks Starkey park they told me to call the Holiday rec center to rent a Pavilion so I assume you would do the same thing call the Holiday Rec Center and you can go there and pay to rent a spot
Ranger Station there upfront after you pass the open fields to both your left & bigger one to your right side. There used to be a pay here station as well, but either call them (best for reservations incase there's an event happening) or meet at the little ranger booth.
I'm not aware if they have that possibility.
They may give you info on their website...we didnt stay
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