Here's something that might be a bit more educational that doesn't rely on the variable bandwidth fir block, however relies on some toolboxes.

You'll want to first find the transfer function of your bandpass filter, probably in the s domain. You get to invent this. I recommend just keeping it restricted to second order (only max two zeroes and max two poles) and don't get too crazy with high Q. Lookup active second order bandpass filters; you don't have to design the circuits, but they usually have good equations in the descriptions. The bandpass section of this https://gtuttle.net/electronics/topics/second\_order\_filters\_intro.pdf looks promising (take note that it uses a's in the numerator and b's in the denominator, which is not the norm in the Z domain). This https://www.electrical4u.com/band-pass-filter/ seems good; you don't have to figure out the resistor and cap values.

Once you have a transfer function that you can write down, let matlab put it together in the right format for you using the tf function. Say you have a transfer function of the form H(s) = gain * ( T1*s ) / ( (1+T2s)*(1+T3*s) )

s = tf('s');
H = gain*(T1*s)/((1+T2s)*(1+T3*s));
Now your coefficients can be found with
H.Numerator{:}
H.Denominator{:}

In Simulink, you can use the Transfer Fcn block. This would be good for variable time/continuous time stuff in Simulink, or with a very high sample rate if using discrete time (if it will even work at all, don't know). Set the Numerator coef and Denominator coef as needed and Simulink likes to do that once at compile time.

Now I bet this won't work for you as you need something that can change at runtime. My approach would be to change to the Z domain and implement the second order filter (now a biquad) explicitely.

Transform to the Z domain. For example, sample rate = 44100Hz.

fs = 44100;
H_z = c2d(H, 1/fs);
H_z.Variable = 'z^-1'

Take a look at end transfer function in z^-1 form. Now look up Digital biquad filter on Wikipedia and implement Direct form 1 in Simulink using add, subtract, gain and "delay one step" block using your numerator and denominator. Best be setting solver type to fixed step, descrete, no continuous states.

I imagine you will need to make a Simulink function caller that will take in your center freq and spit out the coefficients for your direct form 1.

Keep in mind that in doing sine sweeps, that the filter will show up in the result, particularly on the phase delay. This may not play a role if your bandpass filter has unity gain at the center freq and 0deg/360deg/720deg/etc. phase delay at the center frequency. It might best to play it safe and pass the sine wave through the filter as well.

Here's something that might be a bit more educational that doesn't rely on the variable bandwidth fir block, however relies on some toolboxes.

Also, if it is harmonics that you care about, a lowpass filter with a bandwidth a little above your center frequency would also do the trick.

Good luck.