In previous visits to the Kona area, I have seen people camping in the dunes at Makalawena beach, a 20 minute walk N from Kona Coast State Park.
Kona Coast state park is 15 miles N of Kona, but is much closer than
Hapuna Beach SP.

To reach the camping area, drive N from Kona on the Ka'ahumanu highway.
Between mile markers 90 and 91 you'll see the left turn into Kona Coast
State Park.  Drive the rough, sorta-paved road 1.5 miles to the first parking area.  Walk N on the chained-off rough lava road, past some collapsing buildings at a beach, and on across the lava to the next area of coastal greenery. 

This second area is Makalawena Beach.  I have seen people tenting in the area of dunes you first come to.  Bring water and everything else you'll need.  The park closes at 8PM so you and  your car will be locked in for the night.  I'd recommend against leaving anything up during the day unless you're there with it. Closed on Wednesdays.  Nude bathing occurs at this beach so be prepared to see bronzed German bottoms.

I'd strongly recommend that anyone going to the convention get the book "Hawaii: The Big Island Revealed", 2nd ed., 1999, by Arthur Doughty & Harriett Friedman, Wizard Publications.  Get this book and you can leave all the others at home.  Their website is also one of the best sources of info on Hawaii - www.wizardpub.com.  Another website to check is www.konaweb.com.