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My guess would be that any beach camping from Jalama south to Leo Carillo, will be booked already for the dates you have in mind. The only possibilities to get in will be the first come, first served sites that most parks set aside for last minute campers and can't be reserved. Never hurts to call, however, and by-pass the on line reserve system. You'll have better luck if you're tent camping and don't need a site with amenities.