In British English, 'fairly' and 'quite' are interchangeable. 'He's quite short ' and 'He's fairly short' have exactly the same meaning. There is no value judgement involved i.e. no suggestion that this is a good or bad thing. They are merely neutral statements. 'Rather' suggests a negative quality. For example, 'I don't think Roger is likely to get a place on the athletics team. He's rather short and not especially fit.' Note that US English doesn't use these modifiers in the same way as British English does.

With fairly and quite you might be able to depending on what you are talking about but there is a slight difference between the two. Fairly: Indicating to a degree but not completely. Quite: Indicating to a degree completely. Rather: Indicating preference.

"I'm rather tired" = "I'm fairly tired." These are roughly equivalent, though I would consider "fairly tired" more tired than "rather tired." "Quite" presents its own set of problems. "I'm quite tired." will mean roughly the same thing as the above. BUT, "quite" is also used to mean "entirely." For example: You are quite wrong/right about that! (entirely wrong or right) You will find this usage with adjectives that don't present a gradation: think of a whole continuum of being tired, but only two alternatives in being right or wrong.