They want the projector in an enclosure that can (depending on location) have the sun beating down on it all day? That birds can crap on? That people can trip over? (Note that tripping over something is much more fun on a balcony because the landing takes longer than just tripping directly onto the ground.) That his dogs can pee on? That will not in any way fit into any person's idea of "design"? That rainwater might leak into? That snow can pile up in front of?

Find an appropriately sized cardboard carton. Paint it black. Set it in the proposed location on the balcony. Tell him to leave it there and at least twice a day look at it and think about how it looks. Mention all the other negatives. That might cure him of the idea.