There are no DoubleClick events in Silverlight. If you need your custom controls to detect double-clicks, you can record the Datetime.Now value in the Click handler, and treat it as a double-click if the TimeSpan between the two clicks is less than say 500 milliseconds. You might be also able to use the NodeDoubleClicked raised by the Diagram control, if you don't need this for some specific child control of your custom control.

I hope that helps,
Stoyan