What Press Was Used In The 1937 To Mint The Silver Crown

Activities of the Branch mints were attached as appendices to The Royal Mint report. You'll need to find copies of the 1937 and, perhaps, 1936 Reports to see if they mention acquiring or commissioning new presses for striking crowns at Melbourne.

I would be slightly skeptical of them saying it was from the Melbourne mint as I believe the RAM was very very careful with what happened to things once they were decommissioned for example dies were destroyed to prevent forging. Anyway I have found out that they did sell a number of things when it closed in the following article tho it doesn't specify that a coin press had been offered for sale to the public.
http://www.cruzis-coins.com/Grading...rneMint.html
It also states that the RAM bought a number of items so prehaps it bought the presses as well?

The coin presses them selves were commissioned in 1868 and were made of cast iron. Found as well that there are pictures of the British coining presses which most likely would have been used in striking coins here does the diagram match the piece you are interested in?

http://en.wikisource.org/wiki/1911_.../Mint_(coin)

In terms of the value of that crown unless aUNC or better is only really worth melt value and one crown holds bit less than an ounce of silver in it.