I live in Kailua-Kona. I don't know what conditions are like in Pahoa, but tomatoes and green beans grow very well here. Our volcanic soil has good drainage, so I don't think you need to worry about drainage, but you won't know till you try. If you don't have much soil, dig a hole and put a bag of potting or other soil in it. You will probably get leaf miners which won't hurt the plant that much, but aphids are another story and you will need to spray for them if your leaves start to wither. Be sure the tomatoes get lots of sun. Mine do best facing the East behind my house. It all depends on your plot.

I also recommend you contact Kona Outdoor Circle (there is a website) for more information.

Talk to your neighbors to see what they are growing.

I live in Kapoho, just down the hill from Pahoa.
My tomatoes are doing just fine, but they are in large pots. All of my edibles are in pots. Eventually, I'll try some in the soil/cinder, but I don't have a place to put them right now.
It is my understanding (from friends at HPP) that the problem with tomatoes is nematodes, when planted in the ground.
I've no trouble w/ salad greens, again, in a pot.