C.G.
My son was also a binky user. When he was almost 3 we transitioned him to using it only at bed and nap times. My husband and I decided to let him pick the date the binky fairy would come, we let him choose any Friday of that month. On that day, We decorated a boy for the binkys and then had a binky hunt to find all of them from the house/car/bags... Then he placed the box full of binkys in his window and had to go to bed with out it. I think because he has so much control it worked, we had a few rough spots here and there, but he's now 4 and has no problems with his little bro (1) having one. (They are different brands though)
In all, I would say try again in a month or so and give him more control of the process, 3 yr old love to be in control. Good Luck.
C. G