Spray latex paint

Have you considered simply building it out of white melamine (plastic-laminate-covered fiberboard, available at most lumberyards in the US)? Heavy, requires special screws to get a really strong connection, but cheap and durable.

It's unlikely that you'll encounter problems, but it depends on the specific products, of course. Exterior paint isn't exactly rubbery. I'd do it. If the manufacturer or retailer advise against it, use a sealing primer in between.