Yes u can paint the outside back of the tank. Emulsion, etc and paint it a few time. mate's tank has blue paint on as you can see on first pic, but when I took it outside to clean it up the water got into it and it peel off as it was emulsion. But we decided not to repaint it as it look natural with their wall.
Black cardboard hung/stuck just above the water line also does a nice job. Because its not waterproof condensation doesn't form inbetween and when you're fed up with it just swap it out. Best for smaller tanks though.
I used black satinwood paint on my last tank, it's more durable than emulsion, dries pretty fast and doesn't smell as bad as gloss. Put it on with a mini sponge roller for a smoothe finish. Tell you what else looks nice on a marine tank, get some star polyps and dangle them from the surface with elastic bands or fishing line untill they take hold on your back wall, they'll soon spread and cover the back, you won't even be able to see what colour background you've got