if you are up to the php coding needed, you could try using my
http://wordpress.org/extend/plugins/widget-logic/
plugin to get you started. eg you could define a run of widgets, and show one of them based on a cookie (using $_COOKIE) , or just at random. picking at random would use logic code something like:
widget 1
global $my_random_widget; $my_random_widget=rand(1,3); return ($my_random_widget==1);
widget 2
global $my_random_widget; return ($my_random_widget==2);
etc