Print on chipboard in your CD tray
I found a way to print on chipboard with the help of my Cricut. I cut the tag shapes I wanted surrounded by a CD shape. Then I take them off the mat, load them into the CD tray of my inkjet printer and print.
CD printing is highly precise so this also works for printing precisely onto small paper shapes.
Download the chipboard printing templates and instructions here.
Update: SVG version of CD tray insert has been added.