Why not just time the coaster from beginning to end with a POV and divide by the total length of the track? It might not take into account station and transfer track lengths and stuff, but if you're looking for a very crude measurement, you'll get something.
While I'm not an engineer, I would side with chicken.
*WARNING: MATH*
Let's say you have a function (or group of functions) that defines the speed at every given point in time during the ride. You could integrate this to find the total track length.
Now, I may be getting this completely wrong, but the average of a function between points a and b in the domain is just the definite integral from a to b divided by the absolute value of the difference of a and b. Thus, no matter what the actual speed function is, the average should be that same as long as the definite integral between say, start and finish (the track length) in in proportion with the change in the domain (the elapsed time).