What is the specific heat of copper through its phases? Specific heat is the amount of heat required to change the temperature of 1 gram of a substance by 1 Celsius.

For instance, the specific heat of water in the solid phase is 2.059 J/gC and 4.184 J/gC in the liquid phase.

That being said, what is the specific heat of copper in all three of its phases (liquid, solid and gas) in J/gC st standard pressure? How would one figure this out?
The NIST Webbook is generally a good place to look for thermochemistry data. You can see here that there are data for all three phases. It looks a bit daunting, but because heat capacity is not constant with temperature, it's expressed as a Shomate equation. Basically, you find the equation that starts with $C^°_p$ and substitute the parameters from the table underneath along with the desired temperature and you can calculate the heat capacity for any temperature within the range shown at the top of the table. (note that these are molar heat capacities and you'll have to convert if you want it in terms of mass)

If you prefer, you can just click View table to get computed values at certain temperatures, which will save you the calculation.