You could push your closing back a week or so to accommodate him but who is to say that he won't ask to push it back again and again?
Your third option is to close on time then rent back to him for however many days or weeks. As part of the agreement, the seller would have to keep the home under his homeowners policy concurrent with your homeowners policy on the property. You can also get him to pay you 1/30th of your principle, interest, tax and insurance at closing for each day he wantes to stay. It is also your right to ask for an up-front security deposit. During the persiod he is still in the house, you have a sort of renter-landlord relationship. You are entitled to keys to the house, but cannot enter without an agreed-upon notice. Your agent should have a form to handle this, it's called an Addendum O.