Explain to them (paying particular attention to the child) just how much responsibility is involved in caring for a pet. Exaggerate as much as possible. ("Yes, dear, not only will he eat all your toys, he'll always be bumming snacks and shitting and pissing all over your bed. And you'll have to take him outside at least 10 times a day so he can shit and piss some more...")
Remind them (paying particular attention to your wife) of the expense. ("Hey, look at this, honey, one year of dog food costs about the same as 20 pairs of Italian shoes. Or 19 pairs and a nice bag...")
Concentrate on, and reinforce, negative images. ("Dogs sometimes bite little kids, you know..." "Hey sweetie, let's watch this movie I rented. It's called Cujo...")
Never agree to go to the pet shop just to "look". That way leads to your doom. If approached by pet shop staff, make like you're about to pull out a gun.
Never actually "look" at the puppies in the shop yourself. At least don't let your wife catch you looking at them (as you fondly remember your own childhood days playing in the yard with your own dog, and a tear starts to form in your eye, and you want to smash through the glass and scoop up the little puppy with those big, sad eyes and hug him and hug him forever and ever, and... damn, did she see that...?).
Never entertain rhetorical questions of the type "what would be a good name?" or "where will he sleep" or "doesn't he look just like Snoopy?"
Forget all of the above and face the facts: you're fucked...