You can make a clock out of pretty much anything. we've been using stretched canvas frames, but a frisbee works just as well. You just take your fabric, layer it over a piece of batting (makes it look more finished, especially if it is pieced) and stretch it over the frame. If you don't mind making an eyelet or small button hole, putting one dead center through the fabric and batting makes for a cleaner finish.
To attach the fabric to the frame you can simply staple it to a canvas frame, or make darts in the corners so it lies flat at the corners and put a drawstring around the edge to pull it taut. The make a hole in the middle and assemble the hardware. Depending upon what you use to hold the fabric you may find a need to stabilize the clock hardware, the weight can cause a canvas to sag in the center. Consider cutting a piece of foam board to fit tightly into the back of your "frame". Mark the placement of the clock mechanism and cut a hole in the foam board to go around the hardware. Push the foam board into the back of the frame so it holds the hardware in place.
All told, if you already have the fabric in mind that you want to use, you can have a fantastic clock for yourself, or for a gift, in just minutes.