Owner manuals which include parts lists can be downloaded from the Cox Mowers website;
http://www.coxmowers.com.au/operation-manuals/The Series 1 Stockman models are covered by several of those manuals designated by model number only, but yours is later.
You will probably have to try looking at a few of the different Stockman manuals, to see which one matches your machine. The 'New Era Stockman' and 'Stockman Pro' series look to have the same bonnet as your machine.
The transmission it has, will help to determine the model number; i.e. 'live drive' friction disc/cone, as you mention. The alternatives are hydrostatic, or transaxle.