Unless it's dorm-fridge-sized, you can definitely run your refrigerator only during the day, generating ice to cool it during the night. Building HVAC systems often work this way, running the chiller to generate ice during the night (when electricity prices are low or even negative) and running the resulting chilled water through heat-exchanger coils during the day. And superinsulated fridges like Sunfrost models can stay cool during the night even without such extra thermal reservoirs.

A thing I haven't seen, but which ought to be practical, is a solar thermal fridge — for example, using the ammonia-absorption cycle that propane-powered fridges use, but heated with sunlight instead of flames. PV panels are typically 16% efficient, but it's easy for solar thermal collectors to reach 50% efficient, and they're also about five times cheaper per unit area (still). So you'd think it would make sense to power the fridge directly from sunlight.