Sure you can... My daughter was running a day care from a rental home with the landlord's permission and when I lived in Sunnyvale and I was doing the same thing.
Is it going to be a big dfamily day care for 12-14 kids or just a small day care with 6-8 kids? If it is a big family day care, please ask your tenant to get the day care insured. If it is a small day care, your insurance carrier can add it to your home insurance, just to cover all bases.
Actually, having a day care in your rental is a good thing: you can be sure that your property will be in a top shape. Goverment and other agencies are regulary visiting family day cares to make sure the children are in the right enviroment.