Ultimately, you want to find the cause of the green water, such as high phosphates or high light, and correct it...else it may return.
But to get rid of the algae quickly without using chemicals, you have two choices:
UV sterilizer or diatom filter. I researched both options a few months ago.
Both are absolutely, perfectly safe for fish, plants, and biofilters.
UV sterilizer
Pros:
1) Easy to set up and install.
2) Kills algae, fungi, parasites, and nasty bacteria without harming the biofilter
3) Can be used continuously (but see con #3 below).
Cons:
1) Expensive
2) Bulb sleeve must be cleaned occasionally
3) Bulb only lasts a certain number of hours before losing effectiveness. Replacement bulbs are relatively expensive. Again, depends on model.
4) Dead algae must be removed by water changes - results may take a day or two to be noticed.
Diatom filter
Pros:
1) Physically removes algae, fungi spores, and small particles. Actually polishes the water to a crystal-clear state that has to be seen to be believed.
2) Fast - difference seen in minutes.
3) Diatom powder is cheap!
Cons:
1) Filter itself is expensive
2) Harder to set up than
UV sterilizer, but not nearly as hard as you may have been led to believe.
http://www.aquariumadvice.com/viewtopic.php?t=66071&highlight=diatom+filter
3) Must be cleaned after use.
4) Not designed to be used continuously.