"Help, my child is afraid of our pet!!!"
1) Be very understanding with your child & his fears, but know & be assured that it will not last forever. Getting rid of your pet is not the answer!!! This is more than likely a phase... kind of like monsters under the bed. The key is to ease them out of this phase gently & securely so that it doesn't become a lifelong fear. After all, pets are a big part of our society, so they aren't going away... best to learn to overcome this fear as a child than an adult.
2) Get creative in finding ways to make the child's associations with the pet positive & FUN, but never force it. Perhaps use humor? For example, to help a child afraid of a dog, consider putting a t-shirt on the dog for a short period of time and enjoy it as a family ( making sure to involve your child). Say something like, "Look at that doggy wearing a shirt! Isn't that silly?? Do you think he likes wearing a t-shirt? Do you want to go pick out a t-shirt for the doggy to wear?" Next time you might use a bandana. Consider anything that might make the pet appear more friendly & " human-like" as opposed to hairy & scary!
3) Involve the child in a few very simple chores involving the dog, like filling the water bowl & explaining to him that the doggy gets thirsty just like he does. Maybe let him add just a small drop of food coloring in the water to make it fun for your son (and not at all harmful for the pet).
4) If the pet (usually dogs) is overly hyper around your child, consider enrolling the dog in obedience classes (or a lot of things can be taught at home if you already have basic knowledge of training techniques). This will allow you to have more control over the dog's behavior because he will understand basic things like sit, easy, off, get back, etc. You could also teach the dog tricks like high five (usually natural for most dogs & lots of fun for kids) and roll over. When your child realizes he has the coolest dog on the block, he'll most certainly forget that he was once afraid of the dog!
Other Helpful Links:
Helping Your Child to Overcome a Fear of Dogs