You’ll want a pole bean variety. Many out there. Most popular are Scarlet Runner, Kentucky Wonder, Kentucky Blue, Kentucky Lake for green beans. The Kentucky Wonder can be found anywhere like Walmart and HEB and Dollar General. A small package will be more than enough for your space and save the dried pods at the end of the season for next year.
Check out the heights of limas and peas but peas can’t take the heat like beans. Cukes, squash, and melons can also be trellised. I’d go with the smaller squash and melons because of the weight. With the cucumbers, go with one that is both a slicer and a pickler but you’d probably just do some refrigerator pickles due to space so maybe just a slicer.
Tomatoes will trellis, too but go with a cherry because a larger one wouldn’t hold up without caging. Walmart usually has a husky red cherry and a yellow pear are both bite sized. The husky red cherry is really tasty and is a pretty plant. The yellow pear tastes good but isn’t as flavorful, is a good producer and will get wide and grow to the roof if you let but don’t let that scare you off because it’s hearty and can take heat. The yellow pear is a staple in my garden. None of the tomatoes did well last year but once the heat broke in the fall, the yellow pear went gun ho. Both of those are heirlooms.
I’m guessing you don’t have much room so maybe just go with one or two vegetables. If your trellises are separate from each other (as opposed to a grid type across the whole wall), have your son string a couple pieces of wire across to connect them at the top to give the plants more growing room. The green beans, by far, are the easiest to grow as they don’t require much more effort than watering.
Yellow Pears are spitters...Yellow Submarine and Sweet Beverly LOOK like Yellow Pears, but both feature something Yellow Pears lack...FLAVOR.
Thank you. I'm copying your post and saving it. I've looked at Terrior Seeds on the web as we bought some seed from them for my husband a few years ago. Their only sell heirloom seed and they had a section for seed that grows well in heat. Kentucky Wonder was in that group.
I have to get rid of the dead rose bushes along that wall. I tried two days ago to cut them with a manual hedge trimmer and have to get too close to the zillions of thorns. I have ordered a 22 inch machete to whack them down from a longer distance. Once I get rid of the thorny branches, I can pull them out of the ground. I need that machete anyway to whack off zombie heads.