(Note: I know this is off-topic for this thread but I would like to help NFLDERS with the families' new bunny. I considered making it a PM, but figured I would put it out here for anyone else who is interested in rabbit care.)
Happy to help! Rabbits can be very easily litter box trained. They like to go in the same spot all the time. This is because they are naturally neat and tidy, and because instinct tells them not to leave droppings everywhere because they could attract predators. Rabbits should be kept in a large pen when unsupervised (look for a x-pen online or at a pet store). Small cages are not recommended because rabbits have a natural need to move around a lot. If you notice which corner of the pen they generally use as their bathroom, place the litter box there and toss a few droppings into it. A litter box should be lined with pelleted litter that is suitable for rabbits. Cat litter, especially the clay type, is not safe for rabbits. A very good brand is Oxbow. They make a pelleted litter out of wheat that is safe and keeps the odor down. Do not use any type of litter that contains baking soda. It affects the respiratory system. After a layer of litter, add some hay to the litter box. Rabbits like to eat and poop at the same time. It's kind of their thing. If you entice bunny to hop into the litter box with hay, he will likely sit there and do his thing while munching away. If you leave the pen open and accessible while the bun is hopping around, he will have access to his litter box at all times.
The diet for an adult rabbit should be 75% Timothy hay (no alfalfa for adults since it has too much calcium and can cause kidney stones), about 1/4 cup of good quality Timothy-based rabbits pellets per day (Oxbox pellets for adult rabbits are a good quality), and a serving of rabbit-safe greens everyday. Anything with sugar like carrots, apples, or other fruits are considered treats and should not be given daily, only occasionally in small amounts. There are many foods that are dangerous to a rabbit's digestive system including corn, seeds, nuts, even iceberg lettuce can cause painful gas (but romaine and green lettuce are fine). You'll even find packaged foods that are labeled for rabbits with unsafe ingredients (like corn and seeds). Even if there's a bunny on the label, they're still unsafe and not recommended. For a list of rabbit-safe foods, go to
www.rabbit.org. This is the website for the House Rabbit Society and has lot of great information about rabbit care. It also has information on how to identify signs of illness in rabbits. If they don't eat or poop for a few hours and won't accept favorite treats, it's considered an emergency. Rabbits' digestive systems need to be constantly moving. That's why it's important for them to always have hay available to eat. If the system stops moving, they can go downhill quickly and you need a rabbit-saavy vet. Rabbit's are considered exotic pets and must be seen by a vet who is qualified to treat them. Most regular vet offices do not (or should not) see rabbits. It's a good idea to call around now and find a rabbit-saavy vet just in case you need one down the road.
Definitely do not try to put a diaper on a rabbit. Remember that they are prey animals and are always on the alert for predators or any type of danger. They don't like to be restrained and they don't like having anything on their bodies. They get stressed out very easily (to the point of having sudden heart attacks) if they think they're in danger.
Most importantly, the rabbit needs to be neutered if he's not already. Neutering will greatly improve his success with the litter box. It will also improved his health and overall happiness. Because they're prey animals, rabbits have a constant need to reproduce to keep the species going. Males are full of hormones that cause them to be more aggressive, and mark territory by spraying pee everywhere. They're trying to attract females and keep other males away. Neutering gets rid of all of the hormones that make them do that. I fostered two baby boy bunnies who became stinky little terrors when they hit bunny puberty. They went back to the shelter for a week to have their neuter surgeries. By the time they came back, they were such little gentlemen. It takes about a month for the hormones to completely disappear, but these guys were well on their way. They had stopped the spraying and aggressive behavior. They didn't stink anymore. It's also very important for female rabbits to be spayed. If not spayed, 85% will get uterine cancer by age 4-5. It's a sad and painful death that can be prevented with spay surgery in their first year of life.
I know this is a lot of info. Feel free to PM me if you have further questions. It's awesome that you rescued a bunny from a bad situation!