This is an easy pattern. Circles are easy to crochet in general in simple dc, sc, etc.: just keep increasing groupings one more stitch farther apart for each and every new row and the circle should lay flat even if you keep going like that for forever.
All it takes is some pretty patterned paper and Mod Podge to DIY cheap tiles into coasters. You can make them with holiday patterns or something more personalized to the coworker. Get the tutorial at Boxy Colonial.