[susan53]

It´s always possible - but here very unlikely. Notice that here we´re dealing with the third meaning, past action with present result, so the choice is between seeing what has happened as a single event or an on-going sequence of actions. If it were just an explanation of the red eyes, then it´s likely the person would want to express "crying" as something that was repeated - ie went on for a time. Your eyes don´t get red if they just fill with tears momentarily. So the continuous form is the most likely choice ...
-Why are your eyes red?
-I've been crying.

As I said, the choice of verb will depend on the meaning you want to express and that will depend on the context. In this case, I can´t think of a context where the person who´d been crying would want to express it as a single event rather than something on-going/repeated, so I think that 999 times out of 1000 the continuous form would be chosen. But as always, it´s not due to some abstract "rule" but because the continuous form expresses the meaning that the speaker would be most likely to want to express in that situation.

Change to a slightly different situation and you can see how the speaker can easily choose to express either one meaning or the other. Imagine a teenager arriving home from school and his mother talking to him :
- Why are you so out of breath?
- I´ve been running.
(the speaker sees/expresses it as an on-going/repeated sequence of actions)

- Why are you so out-of breath?
- I´ve just run all the way from the bus stop.
(the speaker expresses it as a single event)

Notice that the situation is exactly the same. It´s just a matter of how the speaker "sees" the action and therefore which form s/he has to use to express that meaning.