as afnan said - you are stuck with a dead wall situation. The secondary O2 sensor's only function in life is to measure the performance of the cat. It works on a very small voltage change that is usually between 0.51 and 0.61V.
If your car has a front O2 sensor - its amplitude wave is from 0.1 all the way to 0.9V -as soon as the rear sensor starts seeing this - the ECU knows that the cat is bad.
Remedy - choose one -
install a cat
build emulator for rear sensor
mask the rear o2 sensor with a shroud - like a spark plug adapter on the o2 sensor and hope it works.
The best performance will come out of replaceing the cat, the rest will still cause the noise and silly running.