If I were renting, I would check out the Smart Bags. They're supposed to be good for several growing seasons and I could take them with me when I moved. Don't believe I'd put potatoes in a constantly wet area. Can you ask the neighbors if there's ever been a garden there?

I'm trying something new this year that might work for you.
Culverts are joined together by stout metal rings, Many people use them for fire rings. I'm hoping they'll make good raised gardens. They come in several sizes. Mine are 36" across and about 13" high...somewhere around $25, plus tax. I filled these with a good potting mix and top soil.

I agree, potatoes in wet ground not a great idea. I grow potatoes in containers....basic Rubbermaid 20 gal. Here's a link to inexpensive grow bags. I never ordered any, but was saving the link for when I need it.

Here is a link that might be useful: grow bags

I have poorly-drained ground and I use a raised bed to grow potatoes without digging holes for them, just piling the mulch on top. I also trench around the bed to divert the excess water.

I think if there is never standing water your idea may work well. Potatoes do appreciate constant moisture as long as not waterlogged.

You also might consider laying the potatoes on the soil surface, piling some compost over them, and adding more mulch as they grow.

- N., the lazy gardener

Till, plant tubers on surface, cover and "hill" with straw. The tubers will find the water on their own without sitting in it. You could also mix some compost and straw together and hill with that.

plastic grow bags are your best choice

Here is a link that might be useful: grow bags

Why would buying some plastic be the best choice? Why not save the money and the environment?

Agreed, I have grown potatoes in those heavy tarp bags and they work well.

Just go into Walmart, head to the garden supplies, and you should find them. Big dark green square bags made out of what is essentially roofing tarp material with pre-punched drainage holes in the bottom and a velcro flap on the side.

I ran three of them last year as an experiment, and they all worked like a charm. Was very easy to get the potatoes out of them, and you could even open the flap to grab some fingerling potatoes during the growing season without disturbing the rest of the plant.

Why would buying some plastic be the best choice?

Because these things are heavy duty and will last you for years. A canvas bag I'm fairly sure would rot away after one season, if it didn't rot away before that.