If everyone living in the house doesn't want a dog, then don't get one. That one person will often resent the dog or any 'mistake' the dog makes will cause strain on the relationship.
If you truly want to get a dog and the grandfather is OPEN to trying it out, see if you can be a doggie foster home for a rescue group. This lets you try a dog out to see if it fits your home before adopting plus it provides a wonderful temporary service for the rescue.
I suggest you get an adult dog, something that well-settled and not rambunctious. Usually an adult dog will often already be housebroken in a private rescue and often you'll be warned ahead of any personality issues such as chewing or fear of rubber clogs.
I do not recommend a puppy. You are trying to get someone who is not dog friendly to warm up to the idea of a dog. Puppies, although cute, pee, cry, chew and are general pests until about 1 year to 18 months old. You may think its cute but non-dog people, not so much.
A steady adult dog that is calm and housebroken will be his own ambassator. Contact some private rescues and fill out the paperwork to be a foster home. A doggie foster home gets first pick in adoptions.
You also get to tell them up front what you cant live with such as howling, peeing or severe hyperactivity.
If, however, the grandfather says absolutely not, no pets then either move or live with it. If you are renting from someone, they have the last say.