In this project we will utilize a coffee cup design as the center of the coaster.  I have included this int he design file for the project. 

next, we want to create a ring to enclose the coffee cup design.   To do this, simply add in a circle and ensure the width and height is the same dimension.  I have set mine to 4 inches, which seems to be the standard coaster size.  Next, add in another circle, but decrease the diameter by about ¾ inch.  You can then align both.  Finally, select both and subtract the inner circle from the larger circle.  This creates a single vector that is just ring. 

The settings are for the D1 5W laser.  You may need to adjust the settings for your laser configuration.

Be sure to follow all the safety guidelines for your laser and always wear personal protective equipment when the laser is in operation.