Does the coefficient of restitution change?
It depends on what you mean by "change”.
The coefficient of restitution is based on the surface properties of the ball and surface it collides with. So for a given ball the coefficient will be different for different surfaces it collides with, in this sense it changes. A good example of this is a tennis racquet. The face of a racquet can be divided into different sectors, each has its own coefficient of restitution. The central sector a little above the handle has the highest coefficient. This is what players term the "sweet spot".
Another way that the coefficient can change for a given ball is that over time its internal structure may degrade. This is more the case with balls that are made out of rubber / plastic. Hence worn out balls are replaced during games where appropriate.