I'm doing this right now:
1. TT until someone asks to move out. Say no (or yes if it's the one). Save and quit.
2. TT one day forward for five days after that day. I can GUARANTEE no one will move out within that time I have done this for 7 months and I've never gotten a surprise move out. Do NOT do more than one day at a time, though!
3. TT a month forward, create new character and see the map to see who has moved out.
4. TT back to the original date, load up your mayor and deal with that villager however you like.
I know there are different methods people have done but I suggest sticking to this. It's usually random and if you try anything funny it might screw your chances up.