I would like to keep ice cream overnight, but I only have a refrigerator. When I've tried to store it in the refrigerator it looks like soup the next morning. Is there a way to store ice cream using only a refrigerator. Possibly with ice?
This may seem obvious but you have to keep the ice cream below freezing. Obviously the fridge is too warm.
You could try packing it in ice and salt in a cooler. The ice cream will be soft but not soup. I don't know how much ice would be needed to last all night.
You could put it in a cooler with dry ice. This would be more expensive for the dry ice but would definitely work if you had enough of it.
If you had an ice cream churn you could let the ice cream thaw in the fridge and then re churn it in the morning.
I think the very best way to keep it frozen is to leave it in the freezer at the store and buy it the next day.
As Sobachatina said, an ice/salt mixture will keep things cold for you. A mix of 1kg ice with 340g salt (NaCl) should cool to about -20°C. That's freezer temperature.
See: Cooling baths.
5kg of ice, plus salt ought to hold ice cream overnight in a fridge, especially if you make it in a nonmetallic (insulating) container. Be sure to put the ice cream in a water proof wrap before immersion, or you'll have a salty mess in the morning.