Contact cajon builders directly to find cajons made in Cyprus. Unfortunately most big online retailers and many music stores only carry imported brands. Buying a locally made cajon cyles your income back through your local economy. Below is the link to the one cajon maker in Cyprus:
Minimize the carbon footprint of your cajon purchase - buy direct from the cajon builder. Most imported cajons are shipped around the planet in big cargo ships. A locally made cajon helps your local economy and demonstrates that you are thinking about and support local artisans.
Listed above are links to the cajon drum builders in Cyprus as retrieved by Internet searches in March 2019. I am sure there are many others not listed. Please send me updates and correction if you have additional information. Thanks.