Your best option is to just ignore them. Neighbors moving is determined randomly at 6am when the day switches over.
Hitting them with your net or pushing them into pitfalls does nothing (except maybe make you laugh)
Ignoring them is the only sure fire way, and it might not be the fastest way. --- Don't forget to check out my MegaTen themed webcomics at http://www.drunkduck.com/user/Strain42/ (Currently Updating: Persona 4TW Add-On M-F) 5069-5089-2020
There's no sure-fire way to get a villager to move out (beating them senseless with a net doesn't help your chances). It's all random. But I have found that talking to them rarely and denying favors for them helps. You can't ignore them completely or they'll never do the little *ping* noise that indicates they have something to tell you (when they "ping" you, there's a chance that they'll tell you that they're thinking of moving).
They can still move away even if they never do the ping tell you that they're moving thing. It just might take longer. And having them tell you is sort of a double edged sword because sometimes you'll wish them off and they'll decide to stay out of spite. --- Don't forget to check out my MegaTen themed webcomics at http://www.drunkduck.com/user/Strain42/ (Currently Updating: Persona 4TW Add-On M-F) 5069-5089-2020