Deadbeat tenants will never accept certified mail. Your tenant probably told the carrier that no such person lived there. Keep the mail unopened because you may need to have a judge open it in court one day. Make another certified mail today and post your cure or quit notice on the door of your tenant today. If he finds you posting the notice, you may simply tell him that the certified mail is not working and you are making your post in compliance with your state law. Tell him that he must get rid of the dog immediately or move. The term of the cure or quit notice varies per state. Check it on the internet. But as soon as yours expires you must file immediately for an eviction. Do not tolerate any foot dragging by the tenant. It is not your problem that he can not find a home for his dog on short notice. Once the eviction is filed, follow through with it.