If it's age related, you can talk to them about how their heart has had a life full of love and it's getting tired now. You can read them the rainbow bridge poem (careful, it's a tear jerker).  You can have your child draw a picture for your pet to take with him.. to heaven, or which ever your belief is. 

I've heard religious people say Grandma needs a friend now. So they know their pet isn't going to be alone. 

Please take care. I'm sorry for your loss.