It depends if you have a villager you want to keep at all. If you don't. Try cycling. It really will screw up your town if you don't have beautiful town ordinance on though.
http://http://www.belltreeforums.com/showthread.php?349624-Guide-Cycling-amp-Cycling-Towns-%26%2310141%3B-UPDATE-3-14-16 here is a thread on cycling. This is basically TT'ing mass amounts into the future to land on days which villagers are in boxes, not when they ping, as my personal method outlines.
1. Time travel one day at a time, checking all your outside villagers for pings. (Soon to move villagers will only stay in the town)
2a) If the villager that pings is one you want to keep, memorise their moving date and move 5 days in the future from their moving date (Say Tangy wants to leave on the 15th, you go to the 20th)
2b) If you do not want to keep the villager, and have no intention to give them to anyone, memorise their moving date and move forward five days from that date. (eg, look at example in 2a)
3) Carry on looking for pings one day at a time as usual, or if you're done, simply tt back to the current date. Going in the past doesn't really affect things moving wise, though it's probably a good idea to double check for pings. You should probably check for pings every single day in your town.
extra notes:
- sometimes villagers will not ping you, even though they are moving. Talk to other villagers regularly, as they will usually mention soon movers.
- Sometimes villagers with a low friendship with you will refuse to leave when they ping you. Gross.
- this method has proved really reliable for me, though there's always a risk involved with stuff like this. If you end up losing a villager, you can always get them back. (Not immediately though. You need to do a 16 villager cycle. You can probably look that up.)
- have beautiful town ordinance on. you'll thank me when you have like 5 weeds compared to 50 without it.