I too, had the stringy green beans my first year and I was really dissappointed. I was crushed! They were impossible to chew up! How could something I worked on so hard be so bad?
After that experience, I searched all the catalogs that I thought were from good caretakers of the earth, and found Johnny's Selected Seeds in Maine. I tried their Fortex green beans which are reputed to be virtually stringless. I couldn't agree more! I have grown them for... I think four years now. They are the only green beans I'll grow.
This year, I parallel planted six 20 foot rows. Each row had two rows of seeds running 3 inches apart down the length of the row. The equivalent of two rows of seeds. I was trying for a combination of succession planting and intensive gardening. One month after that, I planted a row straight down the middle of the length of the row.
I planted the first time on April 30th, and picked the last eating beans on July 23rd, 2011. I'm using the rest for my seed crop.
I ended up with 97 1/4 pounds of fortex green beans, which equated to 94 quarts of canned green beans! Everyone in my entire family as well as friends loves them for the flavor and for being stringless.
I highly recommend them. The seeds can be a little pricey, but you pay for what you get in my book. They're worth it!
Here is a link to one of my blog posts specifically about how I did these Fortex Green Beans. You may want to check it out.
http://backyardorganicvegetables.blogspot.com/2011/06/modified-intensive-gardening-combined.html