Hi,
provided the business has an electronic Credit card machine - 99% of places, they will accept credit Visa electron.. I am a UK citizen with a biz in CY, that accepts Electron
But do carry enough cash for a meal as if you find an "off the beaten track
" beach taverna - it is possible they may not have a phone line, so cannot take Credit / Debit / Electron.
I know of several places, Melanda Beach, in Avdimou bay, ( take credit cards, but not electron as no phone line) and Tavernas at Ayios Georgios east of Limassol ( no credit /debit cards )
I'm sure there'll be a few more !
Mark