Not entirely sure what an eye plate or a C-plate are so I'm not quite what hole you're talking about. Is a quick sketch possible?
In general fasteners/bushes in a composite plate have very similar tolerances to holes in a metal plate/sheet. If you are looking to have an interference fit to retain a bush then it should only be from a shrink fit (liquid nitrogen needed; you can't go forcing a pin or bush through a laminate, the risk of delamination is very high, although some people claim to have managed it) and the resulting bearing stress should be constrained to be a fraction of the bearing allowable (often about half), and any additional bearing stress from an applied load should be added to the fit stress (this limit on the total usually provides a definitive limit for the stress permitted due to interference). For smaller diameters this can be quite a challenge to manufacturing tolerances.
If it's just the tolerance on diameter for a clearance-fit bolt then it is the usual sort of thing, a minimum of half a thou up to about 4 thou (0.01 – 0.1 mm) over the bolt's shank diameter. Note that holes in laminates often shrink a bit after drilling, so a larger hole may be needed than is anticipated.
However, if you're talking about the hole in a lug-like part (as pictures of eye plates on the net seem to largely be) then you have a composite lug, which is not at all straightforward. If you've got a load on it then careful FE analysis is probably needed coupled with development testing. However, just the bearing aspects of such a thing would still be similar to my description above, at least for initial work.