My mom and dad are doing potatoes this year and they got those big wooden shipping containers from fedex you could probaly make boxes from old skids and screw them together and they filled it up with dirt and put in potatoes.
I've done it for years. I always have more then I can plant and give away. You can do it in planters, big nursery tree pots, grow bags, trash cans (with holes drilled), etc. I have a whole bed of red norlands coming up, and three 5 gal. tree pots. Just keep adding growing medium, as they grow then dump them out when they die. They need watered more in pots/containers and fertilized.