You could take a hot glue gun and run a bead of glue around the perimeter of the carpet. You can take a needle and close colored thread and sew the perimeter. You could get the carpet glue tape and rent a carpet iron to affix the carpet glue tape to the perimeter. If you have a slit for the table, you could glue Velcro to the carpet and then lay the carpet onto a section of loop to hold the seam together and be able to release it to remove around the table post. It will eventually stop unraveling but remember to cut strings with scissors and not to pull. Pulling will make it worse.