The green is the reference gun to which the others are aligned. In the factory the green will have been precisely set to the centre of the screen with a crosshatch template. Unless the green gun has been physically disturbed or it's centering magnets adjusted, then assume it's correctly aligned and the fault is not with the mechanical alignment of the green gun.
Should you adjust the green without a reference template, you will have extreme difficulty in realigning the other colours to it. Even if you got the static convergence aligned, the dynamic (edge) convergence will be totally messed up, especially, if there is an (uncorrected) underlying fault on the circuit board prior to adjustment. Well..then you'd really be in a mess.
If it's an old rear projection set, then often the electrolytic smoothing capacitors on the d.c. supplies to the convergence board will be favorites to be faulty. They can dry out, leak and go low in capacitance. Sometimes the really bad ones can be spotted visibly, by brown, fishy smelling deposits at the base of the capacitors. In my experience Mitsubishi are particulary prone to leaky electrolytics, (although I still do like their products.)
Another problem for the end user is that the basic alignment controls available to the user are very limited. An engineer with the correct service access codes or (service remote control), will have far more convergence adjustments at his disposal.
So probably best left to an engineer experienced to this type of product, as full alignment can be tricky even for an engineer.
It will probably turn out to be those leaky electrolytic capacitors.
Cobweb, July 2006