Perhaps you can squeeze out a stiffness term for your pump using data from Appendix F of API 610. It states there that, if you remain within Table 2 limits, your shaft displacement will be less than 0.010 inches (or 0.015 inches should you opt for more than Table 2). If you want good pump stiffness numbers, consult your pump vendor.

If you start looking for better numbers here where do you stop? Do you have the right preload on springs? what about other support stiffness and location? what about initial alignment? To ensure reliability in your design you should not use such a sharp pencil in your analysis if you do not have tight control over the final installation.