Summarize:

Rabbits are delicate and do not do well with children's style of handling. Unlike dogs or cats, rabbits cannot cry out, and will resort to scratching or nibbling to show displeasure. Because of this, it's often hard to know if a rabbit is unhappy. Rabbits that are dropped (as children are likely to do) are at great risk for breaking bones, especially their spines. Even though many children love rabbits, they are not a great pet for children. Like all pets, rabbits are not free. They need food, bedding, trips to the veterinarian, and litter (for training indoors). This means hundreds of dollars a year, and more if your rabbit has health problems. They should also be kept in their own area -- don't house two rabbits together unless they are both spayed or neutered and have been shown to be able to get along. This area can be outdoors or indoors. Your rabbit needs to run and hop around and play with toys, typically for a few hours per day. Any outdoor area needs to be fenced and you must watch the rabbit at all times so that he or she is not taken by predators or is able to dig under the fence. This should go down at least 2 feet into the ground and 3-4 feet above ground. Indoors, you need a safe rabbit area (much like you would have for a toddler) with all cords hidden and nothing out the rabbit cannot play with. Many people who initially believe a rabbit will be a great pet for them -- often around Easter -- realize that it is more work than they are ready to take on. It's at this point that many animal shelters have rabbits. Call around to shelters in your area to find out where they might have rabbits available. Often, an animal shelters website will have pictures and links to more info on the rabbits they have.
Do not get a child a pet rabbit. Make sure you can afford it. Check if you have space for a rabbit hutch or cage. Be sure to have space for your rabbit to play. Get a rabbit (if you decide to) from a shelter, if possible.