How can I cool down cooking oil after using it in a deep fryer?

I think it would be reasonably safe to use something like an immersion wort chiller as used by homebrewers. The safety points to be aware of that spring to mind are:

1. Make sure there is no way the cooling water can drip into your hot oil - test all pipe connections first
2. The cooling water exiting the chiller will be very hot - make sure it can drain away safely
3. The exit pipe of the chiller will also be very hot - take appropriate precautions when handling
4. It is possible that the water in the chiller could actually boil. You probably don't want that to happen. Make sure the flow of water through the chiller is fast enough to prevent this. It's probably best to have the cooling water flowing before immersing the chiller in the hot oil.

You can purchase these from your local homebrew store, or purchase the copper pipe and suitable fittings from your local hardware store and build it yourself if you are so inclined.

Please note, I have not tried this out. If you want to try it, I would recommend the following in addition to the above safety notes:

1. Attach a thermometer to the chiller outlet. Never let the temperature rise above 80 deg C
2. Start with the maximum possible flow of water through the chiller before immersing the chiller. Immerse the chiller gradually - one coil at a time - checking the chiller outlet temperature all the time
3. Hold the chiller by the water inlet and not the water outlet, for obvious reasons!
4. If you can, route your output hot water to the nearest bathtub. Enjoy a nice hot bath afterwards while you enjoy your deep-fried treats ;-)

You really can't. The best you can do is put some long stainless utensils in the oil to help dissipate heat, but it's still not going to be fast, just a little faster.

The more surface, and the more cold thermal mass trying to keep that surface at a given temperature the more rapid the cooling - so if you pour the oil into a wide baking or frying pan sat on a concrete or steel slab (or even a cast iron hobplate),or propped up with good or even forced (fan - but i'd want a fan near hot oil like i'd want to immerse the bottom of that baking sheet in water....NOT) air circulation to the underside, it WILL cool more rapidly.

Alternatively, pouring it between two containers (or scooping up and pouring from a height) repeatedly will expose a large and changing surface area of the liquid to air, also giving you cooling.

All these assume you feel safe handling and pouring the hot oil, and that your deep fryer design allows safely doing so.

The oil container has some excess capacity to accommodate the volume of the food you were cooking. You can use that and introduce something cold to the fryer. This can either be a heat-safe solid, like sturdy pieces of metal, or just excess cooking oil. Either one can be chilled thoroughly while you're cooking, then added to the fryer to accelerate cooling.

This won't instantly reduce the temperature to a safe level, but it will help. If you are really in a hurry and have freezer space to spare, you could repeatedly replace the cold metal until the temperature has dropped as much as you want. The metal, of course, will become quite hot initially. Be careful there.

Make sure whatever you're using stays as dry as possible: water will cause bubbling, just like it does when you're frying, and if you're deliberately raising the hot oil level to near the rim of the container, a spill could result.

You'd have to let your oil cool down to 212 degrees F (100 degrees C) first, but you could use the following technique to get it the rest of the way down to room temperature after that:

When I want to quickly cool down stock (for food safety reasons), one of the tricks I often use is to get a container larger than the one containing the hot liquid, and fill it with ice water. This technique would also work for oil, but in this case you need to be very careful to make sure that the container the oil is in isn't hot enough to cause the water to spatter into the oil (hot oil and water are extraordinarily dangerous together), isn't anywhere near full, and that the shape and size of the containers is such that the hot container will not have any chance of tipping over as the ice melts (you don't want the oil container tipping over and spilling hot oil into the water). One way to do this is to put just water in the larger container and then put ice in the area surrounding the sides of the oil container. The water will help conduct the heat even from the underside of the oil container into the ice.

Turn the heat off and wait. There are no safe alternatives.