I would say, ABSOLUTE MINIMUM is:
- 15-18 euro per day in cheap hotel/hostel with private room (excluding high season June-September)
- 12 euro for food (kebab: 5 euro plus water plus breakfast, plus some bread/milk/eggs )
- please note that there is barely any public transportation on Cyprus. So if you need to travel somewhere you will spend a lot of money for that.
So, all together is gives 30 euro daily assuming you do not travel anywhere and you don't come in high season