I know Alpha Phi Presidents have a special badge. As far as KD goes, like many sororities, there is a presidents ring, but either you buy it (and get to keep it forever, which is what i did) or some kd chapters have one that belongs to the chapter and it is passed on to the president each year.
http://www.hjgreek.com/index.cfm?eve...roduct_ID=9012 i have the white gold, and I LOVE IT.
ETA: The ring was my gift from my mother for my 21st birthday, which was just two weeks after I was elected