Center Frequency Shift Bandpass Filter
Your assumptions provide the answer.

If we take R2=R3=R=R4

But, of course, there is no need to do that. Specifically, you can make small changes to R2 to vary the center frequency without making appreciable changes to other characteristics. So, for instance, you might replace R2 with two resistors in series: a fixed R2a and a variable R2b. Setting R2a to 90% of R2, and r2b to 20% of R2 will allow an adjustment range of about +/- 5% around the nominal.