An alternative to containers, if you have the room, is to grow them in mulch, leaf, or "rotten hay" piles. The only drawback I've found is that they won't grow to the same size as in-the-ground slips. We use them mostly in recipes that call for new potatoes.
I like to use rotten hay...the stuff the cows tromp on & ruin, or the outer edges of old bales...just put a pile on the ground maybe 6" thick and 3-4' in diameter, put in the slips, then put another 6" or so of material on top. They grow well with minimal care, a little water & fertilizer. This way you can grow them in bare places in the yard, fence corners, otherwise unusable places, etc.