I think a nice light sage green would compliment the colors of the furniture and dark flooring nicely. You could then pair it up with darker wood accents throughout the room to tie the whole room together.
One thing you might consider is "faux" painting which involves sponging paint on the walls. You can smear it, or pat the paint on with a sea sponge. You will definitely need to practice in an inconspicuous area, but when applied with restraint, the technique can have a great effect.
If the other room wasn't green, I would suggest a rich chocolate brown, and repaint the dining room a warm red. However, if you are unwilling to repaint the dining room, then you are best to go with a warm beige. Beige is always a perfect color because it compliments everything else.
I believe you should paint your living room a light red, a dusty rose maybe. This would highlight your floors and furniture. Plus, this would also compliment the colors in your dining room also.
Choose a color (not white) that shows up against the off-white furniture, complements the green in your dining room, but is significantly lighter than the dark wood floor.
I am thinking of my painting my living room Green with Red as the secondary color under the White trimming. Any suggestions on how that would look, with all netural colored furniture.