Is the Joule Thomson coefficient constant

Defintion of the Joule-Thomson Effect:

$left(frac{delta T}{delta P}right)_H=:mu=frac{V}{C_p}(alpha T-1)$

with the general thermal expansion coefficient (hydrogen behaves almost like an ideal gas in this respect)

$alpha=frac{1}{V}left(frac{delta V}{delta T}right)_P$

and the heat capacity at constant pressure

$C_p=Tleft(frac{delta S}{delta T}right)_P$.

Thus function parameters are temperature, pressure and volume.

It is not a constant for a given gas. A value given in a table must be for some specific pressure and temperature. To see this, look at a diagram showing isenthalps (curves of constant enthalpy). They are not straight lines! However they are pretty straight in the low pressure region when the temperature is comfortably below the inversion temperature. I expect the value given in a table is probably the value at low pressure at some chosen temperature below the inversion temperature.