If you've talked to them to the point they say they're busy and to talk later, do just that. Go watch a YouTube video for about 10 mins or so and then come and spam talk them until they think again.
When I want to raise the approval for my cycling town, I only talk to ONE villager and water all the flowers - "playing" each day will also raise your approval rating. I get super lazy sometimes and just keep TT-ing 1 day forward, until I'm at 100%.
I was stuck on 95% but after I talked to some villagers, it got straight to 100%. I think increasing your friendship with the villagers might help faster.
When I was setting up my weeding town, I asked my friend if I could have her spare normal flowers. I went to her town to pick them up, then planted a load in my new town and watered them, that got my approval rate to 100% really quickly.
Basically everything that the other posters have said. Personally, I changed my town tune, planted/watered flowers, and talked to villagers until they got sick of me.