There are several. Some are native to the US (rough, smooth green snakes...Opheodrys). Ahaetulla are the green vine snakes from Indonesia.They are rearfanged and hard to keep (eating tree frogs and lizards). There are also Thrasops from Africa which resemble Boomslangs. They are sometimes called green tree snakes, though they fall under a ton of different names. They are rearfanged as well. Philothamnus is also a genus of green/vine snakes from Africa. They eat mostly frogs. There are also vine snakes from South America that I believe are of the genus Oxybelis. They can occur as far north as extreme south AZ. I believ that is most of the snakes that could be called greens or vines. So there are quite a few. Most likely you are talking about Opheodrys...the rough/smooth green snakes, but I am not really sure.
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Andy Maddox
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Houston Herp Key
The Reptizone