My condolences in advance. I suspect that you're seeing an adenocarcinoma of the uropygial (preen) gland. I must admit that I have no idea how tizanidine (Zanaflex) would affect a bird. I'm constrained to tell you that only the following is approved by my veterinary association for your purposes:
Euthanizing small rodents and birds at home - from http://www.alysion.org/euthanasia/index.php
When efforts to prolong the life of a beloved pet serve only to prolong death, euthanasia (Greek for "good death") should be considered. Veterinarians have the means and training to put animals which are beyond treatment and recovery to sleep humanely. While the services of a veterinarian should be one's first choice, some pet owners, for a variety of reasons, are choosing not to take their dying pets to a veterinarian. The services of a vet may not be available when they are needed; transporting the pet to the vet might be too disturbing, causing fear and discomfort in the pet's final hours; cost may be an issue. For whatever reason, some pet owners are attempting at-home euthanasia with varying results. The following information is offered, as a public service, to help these pet owners succeed, and not, by mistake or ignorance, add to their pet's suffering by using questionable, untested, or ill-considered methods such as using engine exhaust fumes.
Of all of those methods for euthanasia approved by the American Veterinary Medical Association (AVMA), the only method that could be used safely at home involves the use of carbon dioxide. Carbon dioxide (CO2) is heavier than air and nearly odorless. In low concentrations (7.5%) it is an analgesic (pain reliever), and at medium concentrations (30%-40%) it can be used as an anesthetic, causing rapid loss of consciousness without struggling, distress, or excitation. Medium concentrations cause an aversion responce in some rodents. At high concentrations (>80%) CO2 causes quick death. High concentrations, however, painfully irritate eyes and the respiratory tract, so it is important to first induce an analgesic effect, then bring about deep anesthesia (within 1 to 2 minutes) before exposing the animal to high concentrations. Because the AVMA believes that the flow of CO2 can be regulated adequately only by using compressed CO2, only the use of CO2 cylinders is approved. The following method, being adapted for home use, does not require the use of compressed gas cylinders. The AVMA Panel on Euthanasia has not been asked to approve the following method, and no approval is implied. The author is satisfied that the method is sound and readers should judge for themselves.
The AVMA approves the use of CO2 for euthanasia in most small animals including amphibians, birds, reptiles, rodents, and other small mammals weighing less than two pounds (1 kg). Some amphibians and reptiles, however, may breathe too slowly or be able to hold their breath for long periods of time making other methods of euthanasia preferable. Also some burrowing and diving animals (such as some species of rabbit and marine mammals) have prolonged survival times when exposed to CO2. Also excluded from AVMA approval would be all cats and dogs, even small ones. The methods that follow have been tested only on rodents.
Making Carbon Dioxide
You may have had occasion to mix vinegar (5% acetic acid) and baking soda (NaHCO3) together and see all the bubbles produced. The bubbles are carbon dioxide gas, and 1 gram of baking soda reacts with 15 ml of vinegar (or other 5% acid) to produce 291 cc of CO2. In kitchen measurement terms, 1 cup of vinegar reacts with 1.2 tablespoons (3.6 tsp.) of baking soda to produce 1.2 gallons of CO2, or one gallon of vinegar would react with 1.25 cups of baking soda to produce 20 gallons of CO2. Both white vinegar and baking soda are inexpensive, and using more baking soda than the minimum amount given above does no harm.
You might want to expose the animal to the smell of vinegar to see if the odor is distressing or not. Rodents seem to like the smell. If the pet has a strong negative reaction, you might consider using muraitic acid (HCl) or swimming pool acid. These acids are concentrated and potentially hazardous, so be sure to determine their concentration and dilute them to make a 5% solution first.
If you are at all uncomfortable or unfamiliar with handling or diluting acid, use the white vinegar instead. The CO2 that is produced may or may not have a significant vinegar smell. The vinegar odor question is probably a non-issue, but just in case there is an odor that the animal might react to, you should put some vinegar in the euthanasia chamber so the animal gets used to the smell before the CO2 is introduced.
Making the Carbon Dioxide Chamber
It is best to react the baking soda and acid in a separate container, directing the CO2 through a hose and into the euthanasia chamber, because there is a possibility that the fizzing sound of the reaction might frighten the animal. The simplest chamber is a plastic bag about 1 gallon in size. Put 3 tablespoons of baking soda into the bottom of the bag. Use a 2-cup measuring cup or a 16 oz glass and secure a 3-foot piece of 1/2 inch hose (vinyl hose is sold by the foot in most hardware stores, or a section of garden hose could be used) to the outside of the cup or glass near the top with a rubber band or tape.
Fill the cup or glass with 2-cups of vinegar, and set it in the bag on top of the baking soda. Pull the excess plastic up and wrap it tightly around the hose, securing it with a wire twist tie. Make sure you don't spill any of the vinegar.
The above is quite unwieldy, I understand. Please note that non-avian vets can quickly inject Birdie with an overdose of an anesthetic and Birdie will pass quietly and painlessly. Please respond with further questions or concerns if you wish.