the 2 days method and 2 days back is one of my favourite methods. It is however very unsafe if you have dreamies in your town while doing this method, if you don't do this method properly, you may lose a villager you like, it has happened before.
I recommend before doing the 2 days forward, 2 days back. Find out who is moving first (if it's someone you like tell them no) and then begin the method. This will put this method into a safe chain. ^~^
Other methods, are:
the super safest/slowest method is going day by day. (So go one day forward, one day back, one day forward, one day back) and walking around to see who pings. Tell them no if you like them > tell them yes if you don't. And continue. This method is however super slow.
Good luck~
Also, the current method i'm using. This is my method by the way. It's super unsafe LOL, so I don't think you should try it unless you want to. c:
My personal method;
1.
Find out who's planning to leave.. so what I do is:
go around town talking to everyone. If no-one mentions anything, I just save and quite, TT an hour forward and continue walking around to see if anyone pings. If they do ping and it's the villager I like, I tell them no. Now that I know who just pinged.. Step 2.
2.
I TT 3 DAYS ahead instead of 2. Sometimes the 2 days forward and back method doesn't really work for me since no villagers sometimes don't ping me when I tt 2 days forward, so I go 3 days forward. I then go walking around to see if anyone pings.
If no-one pings. Go to 2a. If some-one does ping go to step 3.
2a) No-one pings. So I go around talking to 3 of my villagers. Yes 3, don't just rely on one. Because the one villager you're talking to could be the one moving so they won't mention in. Keep talking to all 3 until they mentions someone, if they do. Save and quit and enter the game again and walk around the villager that is rumoured to leave and get they'll most likely ping you.
2 b) if no-one pings you even after talking to all 3 villagers, go around talking to more villagers. Crankys and jocks (for me) are quite big gossipers so you could try them! if No-one still talks about moving. Then just save & quit, TT an hour or more forward and enter the game and walk around to see if any other villager pings. Most likely will be.
3.
Someone does ping you - if you like them, say no and continue the method. If it's the villager you're trying to get out, then hurray for you! TT to their move date, get someone to adopt them (if you want or you can just void them) and then TT back to the original date. No consequences as far I'm concerned, unless you have turnips, TT-ing backwards will rot.
.. and yep!
Pretty confusing LOL but if you need more questions, feel to ask me! Yesterday I did my method and it worked pretty well for me, I didn't get the villager I liked to ping me so I keep TT-ing until I reached 2 weeks forward LOL, and I finally got Chrissy to ping! than I TT-ed more to her move date, got her adopted and TT-ed back to the original date, and everything was all goods. So TT-ing backwards no matter how much you go forward, won't do anything bad to your town, except for weeds. This isn't all confirmed an I'm pretty unreliable so eh, if you choose to do my method, go for it! good luck again.
LOL and here's an EASIER summary for you of my method;
find out who wants to move, if you like them keep them. > TT 3 days forward.>find out who's moving, you like them? keep them. >Continue TT-ing 3 days forward
and cycle goes on. <3