This is sort of a neat trick I discovered:
Ok, say one of your neighbors has a furniture item you really want, right? Well, send that person another furniture item of roughly the same size, and they will most likely put the item you sent them inside their house, while getting rid of the other item (The one you're trying to get, hopefully). Later that day, or maybe even the next day, check the recycling bin, and their old item should be there.
I've done this trick a few times, to attempt complete my regal furniture set. I only need one more item of it.