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There is currently no plan to add native Stream Controller (2.0) input support to the "Controller" plugin. As I don't own a Stream Controller (2.0), there would be no way for me to add or test this.

It seems you might be able to run a converter such as "Streamless Controller" to convert your stream controller input to a Xbox or PlayStation controller. 

https://github.com/ddeverill/SteamlessController/releases

While Stream can convert controller input to a Xbox or PlayStation controller, this requires the Steam Overlay layer be added to vNyan. To do this you can add vNyan to your steam library as a "non-steam app". The issue with this is that the controller conversion only happens if the Steam Overlay (and vNyan) is in focus, but if you are playing a game, you will probably want the game you are playing to be in focus and vNyan to run in the background.

"Streamless Controller" seems to convert the steam controller running in Lizard mode to a Xbox or PlayStation controller, and should not require the Steam Overlay layer. If you try this, let me know if this solution works.

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If you are requesting for a Stream Controller prop (3d model) be added to the "Animator" plugin that is possible. Currently you can provide your own custom controller prop:

1. Press the X button on the Animator prop menu to remove the  provided prop. 
2. Using vNyan prop system to add your own controller and move it into position.
3. Create a node graph to activate the prop if the animator is turned on. You can create a simple loop which checks if the animator is ON (1) or OFF (0). Check the xbox_animator_active  or ps_animator_active parameters.

If you have a Stream Controller (2.0) prop, I recommend configuring the PlayStation animation layer (as the layouts are more similar). As the Xbox and PlayStation animation layers are partially-standardized, you can convert your Xbox controller to vNyan parameters (using Shirohane's Controller Plugin) and still make use of the PlayStation animation layer. The plugin will automatically convert Xbox face buttons (X,Y,A and B) to PlayStation face buttons (Square, Triangle, Cross and Circle).