With my oldest children (2½ year old twins), at around 2 years old we started making them leave their binkies in their room when they got up in the morning. I would simply say, "Drop the binky" and they would toss them onto the beds. They used them for naptime and bedtime only. Then one day, we just went cold turkey. I said that I don't know where the binkies are. They cried, but eventually quieted down and went to sleep. After just a few days, they didn't even ask for them anymore.
They still have their lovies, though. I'm in no hurry to take them away. My son actually doesn't even care about his anymore, but my daughter takes Lambie everywhere. Just a few days ago, I started making her leave Lambie in the bedroom, simply because at every naptime and bedtime I had to spend 20 minutes searching the entire house for Lambie! She doesn't mind, and Lambie is now always in bed waiting for my daughter!
Added note: I have 6 month old twins and the older set does not bother the babies' binkies at all. They actually help to give them to the babies.
I hope you find a way that works for you.