Here's the 'before picture':
Easy peasy: I cast on 16 stitches and knitted in garter stitch for as long as necessary. Then sewed the two short ends together, forming a loop to thread on the clock frame. I crocheted around the inner edge and pulled a thread into the back edge to fasten. See my Ravely notes for more details!
And best of all: No threads needed fastening, I just tucked them underneath the edge..
I've created a pattern page for this on Ravelry, so please add your own clock cozy!