First, I never opened the thread about putting down an old hunting dog for fear of what I might read there.
Second, all the folks piling on with the gag threads are probably right to give you a bad time about it.
Third, if you are serious about the best way to put a dog that you love down, and don't just want to read some of the hillbilly or sick and crazy ideas you probably got around here, simply pay a vet for a house call and have the dog injected while you are holding it and telling it you love it.
Really simple and a method that won't leave you asking yourself what the hell was wrong with youself, or having your daughter turn into a stripper because she could never get over you blowing Fido's brains out with your trap gun.
Good luck in this terrible time and I hope your animal is able to pass in peace.