I have favored a super cold ice solution as quicker and less stressful than the slow freezing of a fish put in the refrigerator. Now I have to reconsider this too.

Some people are repulsed by the violence of pulling the fish on a hard surface and making a quick knife cut to the brain. Likewise hurling the fish at a cement wall is quick, but unpopular.

Decapitation can also be quick and effective. But sometimes the disconnected body doesn't know that it is dead and this can be very disturbing to the aquarist.

Putting them to sleep in an expensive anesthetic is recommended but expensive. Sometimes a permit or prescription is needed, as with MS-222 or Tricaine Methanesulfonate. Common brand names include Tricane-S and Finquel and oddly it can be purchased from American sellers on-line. (Disconcerting is the recommendation that the person using it wear surgical gloves and safely dispose of them afterwards!)

Suffocation in soda water has been used too.

Some people will feed the hurting fish to a larger one. That is a "natural" way of getting rid of fish and I have sent culls to a tank of larger fish. I couldn't do that with an old friend though.

Clove oil is gaining acceptance with some aquarists as an accessible and relatively inexpensive anesthetic. Use a drop at a time until the fish is asleep.

One source suggested "Start with 5 drops per gallon and wait about 10 minutes if (the) fish has't gone over on it's side or is deep enough to be worked on add 2-3 more drops per gallon and wait tem more minutes."

Clove oil sometimes is labeled "Eugenol" It can usually be found in most large pharmacies and health food stores in liquid form in small bottles. In one case a guy found it in a drug store as "Red Cross Toothache Medication."

I suppose an overdose of fish shipping tranquilizers such as Hypno, ProTect, Trance, Tranquil Fish Calmer For Bait Fish, Benzocaine would work too. I don't know where you put them afterwards.

I found the following (taken from a note on the rainbowfish mailing list)useful in thinking about the issue of aquarium fish euthanasia. As more data becomes available, the scientific community changes it's thinking on these issues too. I would also guess not everyone would agree with it. Still it is worthy of your consideration:

The Australia and New Zealand Council for the Care of Animals in Research and Teaching have a publication titled "Euthanasia of Animals Used for Scientific Purposes", has three categories of assessment of euthanasia techniques for fish.   These are recommended, acceptable with reservations and not acceptable.

Recommended:
Halothane, MS-222, benzocaine, eugenol, clove oil

Acceptable with reservations:
Injection with Sodium pentobarbitone (Stressful because of need to remove from water)
Stunning and brain destruction, cervical dislocation, decapitation in stunned or anaesthetized fish

Not acceptable:
Carbon dioxide,  Cervical dislocation in large fish, decapitation alone, removal from water, hypothermia/ freezing. (The reason they say the use of cold shock is unacceptable is the length of time it takes the fish to become unconscious.