I would guess that there is something like an universal counter or some data acquisition system that could be able to fulfill your task with some programming.
However, the approach I would use in this case is to design a quick test rig with the following algorithm:
I. Use a fast & stable clock (100 MHz let's say with a <1ps jitter and a few ppm stability) as a timebase
II. Record how many cycles of this signal you count between the each edge of your signal
III. Put that data into a spreadsheet, analyze the results, plot a histogram, etc
By preference, I would implement the counting/recording into a FPGA connected to a PC for data logging and analysis.
Cheers,
Dan