First, you are limiting yourself to state park campgrounds. There is nothing wrong with them, but there is a lot more out there.
Federal campgrounds (USFS, COE, BOR) are a great option.
USFS campgrounds are usually open only during peak season with some being open during the shoulder season on a FCFS basis. Unfortunately, with the extensive fires in recent years, they are very likely to close earlier. And late snows can postpone their openings until as late as July. So it tends to change yearly.
Many of the COE campgrounds are in the foothills. That means they are open year round. During peak season, they are very hot (think valley weather in the summer) and very crowded due to the water sports people (boaters, skiers, jet skiers, etc). In off season, they can be great weatherwise and are far less crowded. I have never had a problem getting a reservation (or even just heading out without one) between October and April. You should check online and make sure the campground you choose doesn't have a closure due to maintenance, etc, as that can happen.
BOR campgrounds are fewer but follow the COE campgrounds.
For me, the most difficult time to camp is August and September. The weather is too hot for me in the foothills and valley areas, and the mountain campgrounds are getting hit by fires and closing.