As far as I have tested it, villager move-outs are random so I don't think there's a way to make that specific villager move away faster (some people suggest ignoring but it has never worked for me personally).
I tt day by day and if Isabelle ever says someone's moving, I'll give them away asap. but if you want a specif. villager talk to them a lot for 1 day then do that for one week before they ping or smth idk
I don't really TT anymore (I never did it to hurry along PWPs ect. Only to get villagers out and get my dreamies in :L) but I never lost a dreamie while doing it. Always talk all of your villagers at least once a day and keep an eye out for the gossip as they sometimes say if someone is thinking of moving. Once you get them to stay then you're safe for a couple of days ~ also check for pings daily :3
You should TT day by day. Don't skip more than 2-3 days. Make sure you get the beautiful town ordiance so no weeds grow in the town while you are traveling through time. Make sure you talk to the villager you want to keep "daily'. Ignore the one you hate, they move out sooner. That's all I have KTHXBAI