There are several types of stabiliser - am i right to assume you want to run the an inline stab. between from your gas bottle into the vertical reg that comes with the cocker? Or replace the vertical reg with a vertical stab?
Either way should work, but since the stab is so consistant, as long as you have an anti syphon on your bottle I would think that just the vertical stab would be enough to give you a very stable pressure into the marker.
Tom