Hit them with the net on a daily basis. And hit them until they are steaming mad at you. *Also you can annoy them with the toy hammer if you can get one.
It does take awhile, I got my annoying villager to finally tell me they were moving after seven days of net whacking, but they will finally tell you they are going to be leaving. And crazily asking if you think they should stay.
I wouldn't bother sending them bad letters because when I was trying to get rid of my neighbor they actually were thrilled that I was writing to them.
I want to try this, but I fear losing another villager.If you want to time travel to get villagers out the safest way is to move forward two days, save, time travel back two days then spend time running around and talking to your villagers to see who wants to leave. With this method you should never lose a villager and be able to control who moves out. But it is random who wants to move out each time.
This is my experience too. I'm currently aggressively befriending Sylvia the kangaroo. I don't really mind her, actually, but could she have chosen a worse position for her house (right in front of the bridge that leads to the event plaza)? I think not.I found that the villagers I am best friends with ask me to move out all the time, the ones I hate never do. My advice, reverse psychology. Become BEST friends with the ones you hate, after some time they will ask you to leave. Currently testing this out with Frita.