Don't yell at your child for asking you - no matter how many times it's been. This is extremely important. Your child needs to know he can come to you any time he needs to. If you shout him away or shrug him off, when it's something important, he may not come to you. Chances are, he's being persistent because he cares a great deal about this potential pet.
Don't just say "no". Explain why not. If you just say no, your child may think you're being mean - and don't be surprised if she verbalizes just that and stomps off. Calmly explain the reasons for not getting a pet. Don't tell them it will never happen. Just be clear on why you can't have one right now. For instance, your home may be too small, you may be moving soon, the landlord may not allow a pet, another family member could be allergic, etc. Your child may try to come up with ways to get around those reasons. Be prepared for that.
Offer an alternative option. Did your child want a cat? Can you get a caged pet instead, like a gerbil or hamster? A fish? If you cannot get any pets at all, think of a family member, neighbor, or friend who has one. Would this person be willing to let your child play with or help care for the pet every now and then? It may actually help that person out if your child takes on some of their caring duties. Plus, it will help prepare him for when he is able to able to have a pet at a later date.