This isn't really an air conditioning question. Those covers are made of plastic. You might have better luck asking a painter what kind of paint to use on plastic then do like the instructions usually say, which is along the line of trying it on a spot that won't show first.

Ok let me restate my questions:

Do these units have completely removable covers that aren't attached to the electronics, or are the electronics integrated into the cover?

Would painting the cover interfere with any sensors or controls?

Are there any models anyone knows of that do have a completely separate cover (no electronics, no buttons, no sensors, etc.) that could be removed and painted without any risk to any part of the unit?

LG makes one that looks like a picture frame, you can put in any art work you like. I can' comment on the quality or repair issues for LG though.

Gee, what a great place to put a picture of your mother in law, with all that cool air coming off the wicked stare,,, talk about realism! :-)

I don't see why you couldn't paint it. There are spray paints available in hardware stores specifically for painting plastic articles. Provided you mask off areas you don't want the spray to enter very carefully (that could be tedious or time consuming for the less patient like me) and either do it yourself or have someone who is good at using those spray painting cans it might be worth a look.

My Sherwin-Williams paint store guy recommended using a bonding primer on the plastic cover, then a finish coat, either spray or brush-on. Obviously, a spray application would require carefully masking for the louvre which is difficult to remove. The cover can be removed and painted separately.