I would recommend turning off the unit and then cleaning it down with some sugar soap.
You can then prep the surfaces with Flood ESP Surface Prep Spray.
After the ESP has dried, I'd suggest coating the unit with White Knight Squirts Spray Paint.
You want to ensure no spray enters the unit. If possible, remove the grill and spray it separately. You should be fine to spray the rest of the chassis in situ as long as you cover the surrounding walls and floor. - MitchellMc
If you cannot remove the unit from the wall, the good news is that it's not necessary. What you do need to do is to mask the areas that you don't want the paint to go onto. This includes covering the sensitive internal parts of the head unit. Your goal is to remove as much of the plastic body as possible so that you can paint it away from the head unit.
However, if that proves too hard, just make sure that the only thing exposed to the paint is the outside body of the aircon head unit. Exhaust ports and infra-red receiver windows must be covered to prevent them from being covered in paint. The surrounding wall and furniture below the aircon must be covered to avoid being sprayed with paint.
My number one tip is to make sure to prep the plastic body as best you can with sugar soap before painting. - EricL
I can definitely recommend using Rust-Oleum spray paint for this job. I've used this product on a number of air conditioners and it works a treat!
Just make sure that you either remove the vent and spray outside or, if you have to paint it in situ, use painter's tape and plastic drop sheets to protect your wall/ceiling from overspray.
You'll be amazed at how well this paint works - your air-con will look like new! If you're not used to spray painting, watch some Bunnings videos on how to hone your technique and have a bit of a practice before you actually attempt to spray paint. Less is definitely more; multiple light coats. - RenoRach1