I called my mom, who has owned a dry cleaners longer than I've been alive, and she said she would quote you an estimate at about $200. She said it depends on the quality of fabric you choose for the liner. A better fabric, which would last longer, will be more expensive. And she agreed with Freedom's post about how time consuming it would be.

Since it is just the liner and people will not see it, patching it would probably be much cheaper and less work.