I have been growing Malibu pole beans the past couple of years and rarely find a string on them. Even mature ones don't seem to have a string. I like their flavor better than Kentucky Wonder, which I grew for years.

Fortex and Emerite are good green beans without strings. Anellino Giallo is a good yellow snap shaped like a shrimp or fish hook. It remains string free up until the pods start to dry.

I like 'full' beans best of all and almost all of them have strings. Some of the few exceptions are Red Eye Greasy, Hazard Fall and Anellino Giallo. - Dick

Here is a link that might be useful: Full Beans

I grow only Fortex now. It has no strings at any stage.