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 is located in Banska Stiavnica.

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.

Playlist of cajons made in Slovakia:

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.