When it's about time for someone to move out of my town, (3-4 days after the last villager has moved out or in) I head straight for the villager that I want gone and avoid running into any other villager. They usually ping me. If they don't ping, then I run around and see if the game has already registered for someone to move out by talking to the other villagers and seeing if anybody else pings.
It's the most reliable method that works for me since trying all the other known methods & I use it all the time.
Remember also that the last villager who has moved in, won't ever move out. Also, villagers won't move out unless you have 9-10 villagers. Oh & a villager won't move out if they're sick so check for that, too.
Edit: Ignoring them won't work since you want them to be able to ping you. So make sure to talk to the villagers you want gone occasionally. Hope this helps!