I have never done a green smoothie diet but I often supplement my vegan diet using fruit smoothies, mixed with vegetables and coconut milk. I have never had any problems using a traditional blender. I suggest getting one of those pre-mixed fruit and vegetable smoothie bags if you are having trouble with veggie smoothies, they usually taste better than anything you could conjure up yourself.
I detail more about this on my blog, if you wanted anymore tips: www.justinbillingsleyarizona.com/how-i-get-my-veggies-in/