When you do self.button = Button(...).grid(...), what gets assigned to self.button is the result of the grid() command, not a reference to the Button object created.
You need to assign your self.button variable before packing/griding it.
It should look something like this:
self.button = Button(self,text="Click Me",command=self.color_change,bg="blue")
self.button.grid(row = 2, column = 2, sticky = W)