I was just about to say that, haha. I've had my eye on her whirlpool bath since she moved in, I want one soo bad! >.< I also like Erik's house, his is very cute.
Olaf, his whirlpool bath was what I wanted, but everytime I came over to try to buy it.. NO! He just did not want to sell it to me or give it to me. :C
I once aimed on Alice's baby bear, I know is pretty common item but I haven't get it in my catalog yet so I went to her house and she ask me to pick anything I like to buy, but she refused to sell me that!! She said is her favourite bear and she need it every night xD so cute~ The bear went along with her when she moved out~ Guess she must really love it.
Next, I aimed on Barold's candy jar that Alice gave him (I knew it for sure), and again he won't sell it to me!! Guess villagers had something they will never give up anyway. But weeks later, I saw him put it up in Retail =3= really Barold? And also I had my eyes on his sleeping bag, but then he never invite me to his house anymore (perhaps because I forcefully keep asking about the candy jar freak him out xD).
Besides this I never really go ahead to get any villager's furniture very badly =x probably because nothing else interest me anymore xD
When they invite you to their house, you can talk to them a bunch of times and they will eventually let you buy something that they have on display. Sometimes, though, they won't let you buy certain furniture items. I don't really know if what they will or will not let you buy is random or based off of rarity, though.