I think carbon dioxide poisoning is a very peaceful way to go. I had a very old pet rat that suddenly became paralyzed one day. The vet wouldn't put him down. I looked up on the internet and followed directions to mix a certain amount of baking soda with vinegar in an aquarium and set the rat in a little box on a towel and slowly add more and more vinegar to the tank around the box. He curled up, yawned, and went to sleep as the high level of carbon dioxide took effect and when he was unconscious I added more vinegar so that the co2 rose to a fatal level. He just went to sleep and never woke up. Very humane. I'm not sure that fish would behave the same way because they seem pretty uncomfortable when co2 rises too high in an aquarium, but a very peaceful way to put down small animals.
I'm glad you researched and figured out a more kind way to euthanize your rat, but I am really disturbed that a veterinarian would not do it for you. That seems really unconscionable. I have NEVER enjoyed euthanizing, but sometimes you take one look at a critter and know that they are in so much pain/discomfort that it truly is the kindest thing to do and have to put yourself and your qualms about taking their lives aside.