The manufacturer may give on low temperature heat capacity for the solid. They will give one melting point temperature if the alloy is eutectic. If the alloy is not eutectic, they may provide both liquidus and solidus.  You will be lucky if they give the heat capacity of the liquid at all. Curves of heat capacity are rare even for the most widely used alloys.

Another source of heat capacities are doctorate thesis. Often, a student will complete a thesis where he measures the heat capacity of a particular eutectic alloy. However, it is unlikely that you will find the heat capacity for your particular alloy in a thesis. You may have to extrapolate from similar alloys.

Alloys that are not eutectic do not have a single melting point. They have a liquidus and a solidus which are different unless the alloy is eutectic. Metal in the temperature region in between come in the form of a slurry. So the metal undergoes a phase transition in this region. Furthermore, its composition changes over the region between liquidus and solidus. The composition of the alloy may be uncertain even after the slurry cools. So parameters like heat capacity and thermal diffusivity are difficult to characterize in alloys.

Again, this is speculation based on my own rather limited experience in the field.

The easiest metals to experimentally characterize may be eutectic alloys and elemental metals. Elemental metals are generally useful because their properties will greatly vary with the impurities and defects in the metal. So what mechanical engineers usually prefer is eutectic alloys.

 I have a question closely related to your own. I can't find the heat capacity for an alloy that I am working with. I want to analyze the alloy at high temperature. The temperature is slightly below the 'melting point' provided by the manufacturer. The fact that he gives one 'melting point' implies that this is a eutectic alloy. However, he doesn't give me the heat capacity just below this melting point.  He provides one heat capacity of the liquid and one heat capacity for room temperature (25 C).

My first impulse is to use the heat capacity at 25 C. However, I know that the heat capacity changes with temperature.  I am considering using the heat capacity of the liquid as my heat capacity for the hot solid.