I've used buckets with drilled holes, earthed up as far as poss: lots of leaf, small crop.

I've used compost bags (Amethyst, if you turn them inside out they don't look as bad), earthed up as they grew, lots of foliage, small crop.

Planted in ground: big crop, but took up all the available veg bed.

Moral of story: spuds need a lot of space!

Also, word of warning: growing stuff on the patio is all well and good but at some point you have to turn it out, so you either need an area of earth on which to make a mess (in which case, plant the spuds there!) or you have to spread out a tarpaulin first, and take care to pick up every speck of dirt or it stains the patio for weeks.

Do you really not have a bed somewhere that you could turn over to growing spuds?