My senior cat has arthritis, poops outside. Is it time to say goodbye?

It's a very difficult decision to make as to when to put a cat to sleep or not, and pain certain is a factor to consider. You've done the right thing by trying pain medications, and I'm sorry they have given him diarrhea. I don't know what kind of pain medication was used, but maybe you could talk to the vet about doing a different kind of pain medication to see if that helps him. Arthritis would make it painful for him to crouch down in a litter box to poop, especially if it's covered. You can remove the litter box top if it's covered to see if that helps. Should there be no other pain medications that are suitable for him and you really feel he is in pain, then putting him to sleep would be the best idea. Examine his quality of life, and if you feel it's poor, then letting him go would be the kindest option. I would first talk with your vet about other pain medications before making this decision. I hope this helps!