Although I have never heard of a "tubing" Cv, that doesn't mean that someone couldn't come up with one. However, based on the principles and reasons as to why the Cv principle was developed, I doubt you will find one.
Basically, the Cv principle is used to rate the maximum flow capacity through a device - a valve, for example. A tube doesn't qualify because you have stated it's principal flow determining characteristics: the I.D., the length, the configuration (is it looped? pig-tailed? straight?)
Until you identify the flow characteristic features, you can't determine an equivalent Cv. Can you be more specific as to where you obtain this tubing Cv criteria? Why would you want to apply it to tubing when you can resort to the conventional method of analyzing fluid flow through tubing: the Darcy-Weisbach relationship?
Art Montemayor
Spring, TX