Cold Turkey.
My daughter lovingly called hers a "Dowdy". I have no idea where she came up with that.
Mine was an addict. She only got it in bed from about 16 mos old, and knew if her feet were on the floor, it went right in the trash, but I swear she manufactured the things in her sleep! We had her talked into the day she turned 3! That was THE day. She was all geared up for it. I knew where they all were (we were down to a few..I hadn't bought any in a year).
I was a Nanny then and she had her own little room to sleep in, and a Dowdy on the bedside table (she had been in a "big" bed since she was 22 mos old). We hit nap time at work, the kids I cared for were 5 and 8 and were in on the pep talks for weeks before this day. We all cheered her on when she put the Dowdy in the trash, went to nap easy as normal (she had other addictions to see her thru it all...a Blankie and a Beanie Baby).
That night she went to bed no problem as well (we had already tossed the home Dowdy out after she got up that morning). Well....next day..day after her Birthday and its now naptime at work. "Momma, I need my Dowdy!". "Um..No...remember you are 3 years old..a big girl now..no more Dowdy..remember?"
"But Momma, my birthday is over and done now. I get my Dowdy back now!"
OMG...4 nights of H*LL after that...but no more Dowdy.
Good luck!