As has been indicated, overdose of anaesthetic gas is difficult and prolonged in reptiles because of their metabolism. Injectable euthanasia is difficult in the little ones (and even in larger ones) because of how hard it is to inject into a vein or the heart. It can always be accomplished by injecting directly into the body cavity, but does take time to produce unconsciousness that way and some would argue that the trauma of being handled, manipulated and injected contributes to an inhumane death. It remains the most accepted humane method if performed by an experienced veterinarian, but barbiturate drugs are restricted and not available to unlicensed individuals.
Most breeders use freezing and it is considered 'acceptable' but this is debated by veterinarians and groups responsible for animal care criteria because it is not possible to be sure that the animal becomes unconscious rapidly and so does not suffer before death takes place. Brain activity consistent with consciousness can be taking place in animals during the freezing process. They are cold blooded, but what that means is that they seek to regulate their body temperature to what is ideal (mid 80s) by finding the right environment - when they experience cold, they seek warmth - so one could argue that being put at feezing temperatures causes suffering. It does mean that you don't have to use a hand's on approach and you don't have to see the animal die - guess for some people that makes it easier.
Decapitation also is not confirmed to be a humane or painless death because of the capacity of the brain of cold blooded animals to register activity even when separated from blood supply.
As brutal as it may appear, the suggestions of severe trauma to the head, effectively destroying the brain, are the most humane. This has been confirmed by various councils on animal care that indicate the approved methods of euthanasia for research institutions. It is critical that the method chosen results in complete and rapid destruction of the entire brain (mostly the cortical areas), so it has to be done with care and precision - not just smashing the animal's head and hoping that you get the right area.
We euthanize reptiles by using a pair of pliers to crush the skull just behind the eyes, by squeezing the head in the vice end. Select pliers with a flat, wide grip to insure even and rapid pressure. The crushing tyically results in massive firing of many nerves at once and there is reflex movement of the body (contractions and twitching) for a few minutes. The brain tissue will sometimes be forced out the nostrils, which is messy and makes the method difficult for some people to perform. Despite the fact that it may seem brutal, it is, in fact, humane (rapid unconsciousness and rapid death). There is no doubt that the brain is destroyed quickly.
best of luck making a decision for your little one - something all keepers must face at some point,
mary v.