Splais,

this si getting a little complicated. I have given you the method for finding the Centre of mass from the front of the aircraft and the position of the Centre of mass from the fuselage longuitudinal axis.
You need the height. '
This is easily calculated as well by using the principals of SImple Harmonic Motion. Think of the plane as a pendulum. Its centre of mass is suspended from a string of length L

If you could get the opendulum to swing about the CG position as defined by the distance from the nose of the aircraft you could suspend it or support it under the wing at that point, CG point. This should not be too difficult to do. Yes I know its 50% scale but it just needs to be lifted a few centrimetres so that it can swing unimpeded.
Once the plane is suspended on that linei t will rock back and forth if a force is applied to it. You know the mass of the aircraft I hope. if not the total mass is the sum of reaction forces at the wheels or the sum of the three weights recorded at each wheel when the plane has been <u>levelled.
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Now all you need is a stop watch. the formula is:

L= (T^2 x g) / (4.pi^2)

L = length of your pendulum or the distance of the pivot point to the centre of Mass.
T= is the time period for the plane to rock one complete cycle
g = acceleration due to gravity, assume 9.81 m/sec^2

Once you have the answer, this will please your scientists greatly and they will laud your ingenious application of science. After they reward you you can buy me a special gift from Tower Hobbies next sale

Unfortunately the methods proposed in previous posts that entail tipping the aircraft  and drawing lines will tell you little. but you will have some fantastic racing stripes all over your fuselage.

If you have time, do some reading on simple harmonic motion. You can actually find the cente of mass of a aircraft simply by suspending it and apply a known force and measuring its displacement in 3 axis.
Unfortunately with the advent of CATIA, PRO/E and the like, these techniques are seldom used</p>