I have not replaced a pump.
The cycling is concerning, that means there is a leak somewhere in the system. It may or may not be the pump. If it is the pump, the diaphragm (p# 94-800-01) could be the issue. However, if you have a small leak anywhere in the pressurized side of the system, the pump will cycle as the system looses pressure. I have experienced this many times.
Have you verified the issue is with the pump? You can remove it, bench test it, and buy a rebuild kit if needed. The diaphragm for that pump on Amazon is $18.
I believe this link is the manual for your existing pump. The parts list is on page 3.