The Kings Island campground is gone, alas.
There also are a few little private campgrounds around Fort Ancient (a couple exits north on I-71); Morgan's is the closest, I believe, and also has a canoe livery if you want to canoe the Little Miami River.
Other state parks near Kings Island to look into are Cowan Lake (937-383-3751) near Clarksville (very nice!), and Stonelick State Park (513-625-7544)
near Pleasant Plain. Both -- as well as Caesar Creek -- are maybe 20 to 25 minutes from Kings Island.
Happy Camping!