Vibrato audio effect circuit
At first glance this could have been easy if you were doing a tremolo.
The vibrato on the other hand is quite hard to achieve.

Have you looked already at some guitar pedal implementation of the system such as the BOSS VB-2. It shows the building blocks of what is required for this to work.



My understanding it that you need an oscillating signal with its Rate and Amplitude (Depth) (IC5, IC4, IC3) to control the frequency shift introduced to the input signal by IC2.

The frequency shift is obtain by modulating the length of a delay line, which thanks to Doppler effects introduces a frequency shift (IC2 is a delay line), imagine turning the time knob of your delay pedal, you get those stretching/compressing of the signal which changes the pitch.

Do this in a sinusoidal fashion and you get a vibrato.

Both clean and wet signals are then added/filtered together by IC1 to get your final signal (clean on the non-inverting input, wet on the inverting input)

There is also a lot of filtering/amplifying that is out of the scope of my understanding. Also the rise time circuitry I don't really understand its fonctionnality.

Try to understand the basics of the delay line modulation, the rest is application specific.