We have standard 4 inch round and 4 inch square with rounded corner dies for coasters.
We do not print CMYK process work. Offset or digital printing will be better options for this type of artwork. We only do letterpress printing.
Rather than a beverage mat we use an absorbent blotter stock. Beverage mat board stock is great for coasters, but not great for deep impression letterpress. The surface tends to cracks under heavy impression.