'Tinting' the windows or something will only make it darker. BUT, as a long-shot of an idea, there are these relatively new 'windows' (but not really windows) called Solar Tubes. In short, it's a fairly large tube that 'gathers' sunlight from the ROOF and 'reflects' it downwards to the room below. 1) It doesn't need to be installed in a straight line, 2) it mounts in the ceiling, 3) you can buy 'shields' for them if they're too bright, and 3) they're relatively easy to install and not that expensive. This idea is just a thought.
I know there are florescent-type bulbs that mimic sunlight pretty well. We have them in our building and are pretty nice. You may want to look into that. I'm not sure what 'scale' they manufacturer these bulbs on because ours are 4' bulbs. (Kinda BIG for a home.) Maybe they make them smaller for lamps, I don't know.
I wish I had more to offer. Maybe over time, since your neighbor's wall gets direct sunlight, it will fade. The OTHER good news is that the 'color' should vary as well depending where the sun is in the sky. For example, I'd suspect you'd have less of a 'green' in May, June, July, and August because the sun is fairly 'high' in the sky. In the remaining months, it's lower, thus, reflecting more directly in through your windows. Heck, for all I know, maybe there's a 'film' that absorbes reflected, green light! Check with window installers, you never know.