CAPE-OPEN

Error using CapeOpenUnitMex, Failed to calculate jouleThomsonCoefficient.Dpressure: The specified property "JOULETHOMSONCOEFFICIENT.DPRESSURE" is not recognized.

This implies that the thermo server you are using does not support this property.

Not many, analytically, I suspect. The JT coefficient is dT/dP (constant H), or (dH/dP)/(dH/dT). H itself is typically calculated from a temperature derivative of some form of the chemical potential (e.g. the temperature derivative of log activity coefficient or log fugacity coefficient) so the first order derivatives of enthalpy already require second order derivatives of log fugacity (or...) coefficient. Hence, the first order derivatives of JT coefficient would require 3rd order derivatives of log fugacity coefficient. Perhaps some engines implement this, not sure.

Similarly you will not often find the derivatives of heat capacity, as heat capacity itself already represents an enthalpy derivative.

Of course approximate values can easily be calculated by using a perturbation scheme.