first, you'll need to get another new villager, as the last one to move in will not ask to move out
after that, it helps to know the mechanics of how villager move-out requests work (these numbers assume you have 10 villagers)
if a villager asks to move out and you say yes, nobody else will ask for 15 days. if you say no, nobody else will ask for 5 days. the day after a villager asks to move out (no matter what you said), the chance of another villager asking to move gets reset to 50%, and goes up by 1% each day that nobody asks up to a maximum of 80% (though for the first 5/15 days, that % gets multiplied by 0 so nobody will ask)
the trick to getting a villager out fast is to not answer move out requests from villagers you want to keep. if a villager you like is doing the thinking thing, and you think they might ask about moving, wait for the saving icon to appear before talking to them. if they ask about moving, quit the game without giving them an answer and don't talk to them the rest of the day. the next day the game will re-roll to decide if someone else will ask to move. this way the counter doesn't get reset to 50% and you don't have to go through the 5 day period where nobody will ask, so you can get the villager you want out to leave faster
lower friendship makes them more likely to leave, but the difference isn't huge so don't worry too much about it. you should at least talk to her once in a while so that she doesn't get stuck on introduction dialogue or "I haven't seen you in ages" dialogue
Visit my dream towns!
Angie from Maplerow, Ranae from Wayfield and Olive from Yorkwood