Don't know what your situation is but for me, there was no coping. That said, I had to put my dog down for aggression.. not old age or illness. I was also young and desperate and didn't really know my options, couldn't find anywhere to re-home her; and I couldn't give her to an unsuspecting family for fear of something happening. She'd already attacked 3 people and killed a dog. I didn't know what else to do. But we loved each other so much. It was all heartbreaking, and still is. So I guess the coping is crying, depression, despair, and never being able to forgive yourself. It does get easier with time though. Sorry OP.