Tranzmetro‘s new Matangi trains have an internal width of about 2.4 metres, and a bike on average is 1.8m long, so parking on a slight angle will give plenty of room for a bike to be stored on a train.
Copenhagen’s S-tog trains have a carriage in the middle of each train, with a one way system, where you enter with your bike at one end of the carriage, and get off at the other.
The inside of the carriage looks like this:
Bikes on trains are an important part of integrated transport, and should be encouraged by making it easier than it now is, be for way more than 3 bikes per train, and should be available for all services and not just off-peak. If crowding is an issue increase the frequency of service. It is more cost effective to increase the cycling options between Kapiti and Wellington than to build a billion dollar motorway for 3.25 billion dollars.
Info from the Cycling Embassy of Denmark.