Instructions
Travel to a friend's town via Wi-Fi Internet connection to increase both the likelihood of having an animal move away from your town and having a new animal move to your town. Likewise, having a friend visit your town via Wi-Fi will have the same result.
Talk with the animal neighbors while visiting another town to build a relationship. This increases the likelihood of a new animal moving to your town. While in town, write letters to the animals you meet and include small presents, such as fruit, to strengthen relationships. Accept requests to run errands and play games with animals in another town when they occur.
Ignore animals in your town that you want to move out if playing via Wi-Fi is not an option. Even negative attention will keep the animal around longer, so refuse to talk to them whenever possible. Check each animal's house every day to see if any are planning to move. If their furniture is boxed up, they are planning to move the next day. If this is the case, do not convince them to stay or talk to them any further.
Maintain your town's happiness rating to attract new animals to the town. Even if you have less than eight animals, you may not receive new neighbors if the town is overrun with garbage or weeds. Check the town's rating at Town Hall to see what needs to be improved. You do not need a perfect town rating, but it cannot be poor.