How do I kill an aquarium fish in the most painless way possible?

I have a pair of silver dollars. They are almost 11 years old and have been living in a 55 gal fish tank their whole lives. By now they are a part of my family and one is getting to die. ( I am a big fisherman, I know what it looks like for a fish to die) Both have intense head rot, color loss, fin loss and for the most part they have always been going strong. One of them is getting a little stiff looking and he seems like he's suffering a lot of pain. How can I put the palm sized fish to sleep? Will it work if I place him in de oxygenated water for a couple hours? I need help.