Designing a Notch filter for Digital Audio to be able to work with all audio sampling frequencies
What you want is impossible. The notch frequency is always relative to the sampling frequency, so you design a notch filter with a given ratio $f_{notch}/f_s$. What you need to do is design different notch filters for different sampling frequencies. The same is of course true for cut-off frequencies of frequency selective filters, center frequencies, etc.

By the way, considering computational complexity, IIR filters are usually better for implementing notch filters than FIR filters.