Our Olive has resolutely refused to take a binky. We haven't encouraged it, but, on occasion, we would offer her a binky when she seemed to need some soothing. It was always rejected, often by an emphatic spit across the room. We stopped making the offer and put the binkies away.
As I unpacked Olive's boxes, I came across the binkies and put them in her box of outgrown clothes. Olive plucked one out and stuck it in her mouth. There it remained all afternoon. In fact, her new binky-interest persists.
I'm not pushing it too hard. (But, binkies don't go to school. There was a minor tussle this morning.) We've had lots of recent turmoil and a few sucks on the binky doesn't seem like the worst thing we could permit her.
She also found (and I put on her) the super cute apron her Aunt Jen made for her. It is a tad too big yet but should fit nicely before too long!