FIR design : compute coefficients for the same frequency response at another sampling frequency
There is no direct way of converting filter coefficients between two sample rates while maintaining the exact transfer function (at least where it's properly defined). 
Re-sampling the impulse response can be done but will often result in extra latency, a longer filter, and some change in the frequency response.

In this case, however, you can derive the original filter specification from the filter coefficients and than re-design the filter using the same specification at a different sample rate. By visual inspection we can find that the ITU filter is an equiripple filter with


pass band edge: 20 kHz
stop band edge: 28 kHz
pass band ripple: 0.1dB
stop band attenuation: 40 dB


Let's say you want that filter at 4*44.1kHz instead of 4*48kHz. In Matlab you would do the following: 

%% match the filter at 44.1 kHz
fs = 4*44100;
d = fdesign.lowpass('Fp,Fst,Ap,Ast',20000,28000,0.1,40,fs);
hd = design(d,'equiripple');
% convert to polyphase
h4 = 4*reshape(hd.Numerator',4,12)';


and the coefficients would be

    0.0057292     0.001552   -0.0015723   -0.0049864
   -0.0056096   -0.0017098    0.0050592    0.0099256
    0.0080942   -0.0011323    -0.012505    -0.017267
   -0.0093558    0.0088501     0.025828     0.027239
    0.0063161    -0.028386    -0.054115    -0.045155
     0.011432      0.10497      0.20287      0.26531
      0.26531      0.20287      0.10497     0.011432
    -0.045155    -0.054115    -0.028386    0.0063161
     0.027239     0.025828    0.0088501   -0.0093558
    -0.017267    -0.012505   -0.0011323    0.0080942
    0.0099256    0.0050592   -0.0017098   -0.0056096
   -0.0049864   -0.0015723     0.001552    0.0057292


However, there are a bunch of potential problems: 


In this case we simply lucked out that the number of coefficients for the new sample rate was 48 as well. In other cases you may have to adjust the stop band frequency to dial in the desired number of coefficients.
This particular filter specification has been derived from the original sample rate, i.e. pass band and stop band are symmetrically spaced around the Nyquist frequency of 24 kHz. That is intentional. If your sample rate is different, you need to understand WHY it is different and whether the original specification is still appropriate. In the case of 44.1 kHz you may consider placing pass and stop band symmetrically around 22.050 kHz and maybe also consider lowering the pass band and/or increasing the number of coefficients.