If you move to the South of Cyprus there are no difficulties in settingup in business if you are EU citizens (which I assume you are). As Cyprus is a member of the EU any EU citizen can start a business.
It is wise to do it legally though, as in paying your taxes and social insurance as the social insurance is now gunning for anyone who tries to get aways with it. The penalties are severe if caught so it isbetter to do it properly from the word go.
The good thing is that if you are paying social you dont need to have private health insurance and also you will be entitled to retirement pension from Cyprus when the time comes.
Veronica