Allergic reactions can cause cherry eye, so can stress, but usually if this happens they do go down.
True cherry eyes are due to a lack of stregnth in the third eyelid muscle. You can re-tuck it, but it will just come back out. The muscle is not strong enough or has too much elasticily. So I would say that a true cherry eye would not benefit from a diet change. However, cherry eye or not, a good diet should always be chosen.