Nickel plating with nickel acetate, nickel chloride, sulfur, saccharin and coumarin
The formula calls for nickel sulfate; is it possible to simply add the powdered sulfur to the solution, or do I have to use a different process to synthesize the nickel sulfate? 


This will not work. Sulfur ($\ce{S}$) and sulfate ($\ce{SO4^{2-}}$) are two pairs of shoes. The oxidation state is different and there is no way that sulfur powder will turn into sulfate during the electroplating.


  If so, can I do so with the materials that I have?


It might be possible to heat another nickel salt in sulfuric acid, cool down and wait for the nickel sulfate to precipitate, but I wouldn't do it!

Given that the nickel salts are highly toxic, might cause cancer on inhalation and are harmful for aquatic organisms, I wouldn't mess around with crystallisation and the remaining solution for which you would have to find a safe way for disposal.

It might be much easier to aquire nickel sulfate and set up the bath for electroplating according to the given specifications.