Contact cajon builders directly to find cajons made in Slovakia. 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 are links to 2 cajon makers in Slovakia:
Rebel Cajons are located in Trencin, Slovakia. Pisch Percussion, also known as Cajon.sk is located in Banska Stiavnica.
You may be able to minimize the carbon footprint of your cajon purchase by buying a locally produced cajon. Check out this link to learn more Mitigate Climate Change . 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 Slovakia as retrieved by Internet searches in March 2018. I am sure there are many others not listed. Please send me updates and correction if you have additional information. Thanks.