Magnetize a thin cobalt steel rod
The Curie temperatures for iron and cobalt are 1043 and 1400 K, respectively, which suggests that an electrical heating system may not be your best bet. If you do, a capacitive system would seem the worst way to go, since the amount of energy will be pretty high.


  How would I calculate the coil wire size needed, and number of turns?


For what? Are you planning on trying to make an inductive heater? If the coil is to be used for producing the magnetizing field, that depends entirely on what field you want to produce, and you haven't specified that.


  How would I confirm success?


Put your rod near a magnet, and measure the attractive or repulsive force.