Hi All,  This is an interesting question!  However, I think we need
a little more information before an accurate answer is forthcoming.

Question: What sort of tubing is in the piano?

I ask because I've seen all sorts of tubing in player pianos, and in
all my years in business the only players that had any smell of rubber
came from units that had non-standard tubing, i.e., automobile tubing.

Another question that comes to mind is: Has the player been
electrified?

I only ask that question because I've noticed strange odors in units
that are electrified from time to time.  Typically, it only happens
in units that aren't used very often.

And a final question: Does the problem occur all year long, or only
when the weather gets very hot?

Here again, I would suspect any non-standard materials that were used
in the instrument.  (It's like my car.  During the colder months, the
car has almost no noticeable odors.  However, during the heat of summer,
and after driving at highway speeds or in heavy traffic, there is
a noticeable smell of rubber.)

Musically,

John A. Tuttle
Player-Care.com
Brick, NJ, USA