Thanks! Here's an easy way:
-befriend them as much as possible, the game wants us to become friends before they even decide to leave
-every 4-6 days (usually 5) a villager will ! and tell you they want to leave (say ok or no)
-go to the date they wanted to move; if you said no, repeat the cycle and run around for others to ping, and/or talk to snooty and cranky villagers and they'll tell you who's rumored to move if you need help on finding them. If they don't ! you right away, just save&quit, and try going to them again
-repeat this til you get your unwanted villager to !, then tell them to scram
Phew, hope that helps