Yes, you can rent a table and hammock for your bags!
There are several umi-no-ie (seaside structures) on the beach on Shiraishi that will rent you shade. For 500 yen per person you can have a nice place to sit for the day and even bring your own food and drink. The Moooo! Bar also offers this service. We provide a table (can fit up to 8 people) and a hammock. The fee includes the use our changing room. Of course, you can also have drinks and desserts from the Moooo! Bar and Calfe delivered to your table.
It's an interesting cultural difference, but the Japanese tend to rent the tables and use them to put their stuff on. Foreigners, on the other hand, sit at the tables and put their bags and stuff on the sand.