Teflon plumbers tape from the hardware or grocery store, a Qtip or two, and maybe some dental floss are all you need for an emergency tenon cork repair.
Unravel some cotton from the Q tip and pack it in the area with the missing cork.
Wrap the tape around the cork and cotton several times, pulling firmly as you go.
This will get you through until you can have the cork replaced. You can also use dental floss wrapped around the tenon to replace a cork that is completely gone. Teflon wrapped around the dental floss will make it feel more smooth.