Hmmmmm interesting topic for a change.
I think you need to look at the facts of the case.
The person is asking for a charitable donation to benefit a sick child. This cause is one which many would feel motivated / duty bound to contribute to.
If the person was asking for money for organised crime or crack would you still support the cause?
If she was asking for cash as she was living on the street then you would make your own decision based on your own circumstances as to whether or not you'd want to give her the money and how much.
If there is no sick child and this is nothing more than a scam then that person is a cheat and a criminal. They have fabricated a story in order to obtain a benefit.
This person is EXERTING FORCE on others by utilising emotional blackmail in order to OBTAIN CASH under FALSE PRETENCES.
It's irrelevant as to whether or not she has a genuine need. By lying about her motives she has deprived 'us' of our right to make an informed decision. Her story is engineered to appeal to the widest audience and could possibly entice individuals to give far more than they would usually do in the belief that they were supporting a desperate and life-saving cause.
If Cyprus has laws regulating the collection of charity on the streets (ID cards, licence, official collection boxes etc.) then they should be enforced (I'd hazard a guess that such laws are in place but happy to be advised).
If not, enquire as to which hospital / hospice or whatever the kid is resident in and make a direct donation. Saving the person on the street the possibility of becoming a victim of crime and having her takings stolen
Personally I'd report her to the police and let them sort out whether or not she is telling the truth. May do her a favour in the long run.
Make direct donations to your favourite charities or only support official organised charity events.
IF you still feel guilty about whether or not she is 'in desperate need' herself and believe that she's only doing this as she's too proud / embarrassed then sleep tight in the warm fuzzy knowledge that there's charity's out there that CAN help her.
The POLICE SHOULD point her in the right direction (after giving her a few free nights food and lodging for being a lying so and so ....).