The State Library of NSW contains a set of architectral drawings of the original and buildings from Luna Park Melbourne. They also hold drawings from LPS and also LP Glenelg (SA).
For at least the last 40 years, LPM has a only had 3 sets of trains, allowing a 2 train operation. The train storage and workshop was at the rear of the river caves. Once upon a time you could see into this area when arriving into the unload area of the station.
LPM confirmed to me recently they have 3 trains. Red and green which are currently in service. The blue train is currently being refurbished.
In the past, the train colour schemes have varied. At one point, at least 1 of the trains was a mix of red and yellow.