FastCap, a company started for making adhesive screw cap covers, also has a kit that lets you make your own covers out of .018″ to .022″ thick edge banding or veneer, but they don’t recommend plastic laminate.
To make your own covers, apply the speed tape to the back of the veneer. Then, with the right size die in the hole punch tool, punch out the covers from the veneer. Now you have covers that will fit perfectly into the counter bores created by FastCaps Flush Mount Drill System.
You can purchase the Custom Color Punch kit for $80 which includes the punch tool, a 3/8″ die, a 9/16″ die, a 18mm die, a 1″ by 50′ roll of SpeedTape, a 9/16″ flush mount carbide cutter, and some sample PowerHead screws, all packed into a hard plastic case. Individual replacement components are also available from FastCap.