Google the model make brand & you may be able to get a replacement part for it. That failing, I'd be dodgy & just hit it up with spray paint. Take it to your local hardware & ask them what you can paint it with.

I also think worth contacting company to see if they do alternate covers.

I wonder if it could be vinyl wrapped at an auto place? Just re-cutting all the vents would be tedious!! Would you have to recolour the body of the unit also though?

I've seen some neat solutions online by building a box frame around the unit and making 1) a removable cover or 2) a permanant vented cover like example in link below. That was for an older style wall unit situated midway up the wall. The slim units like yours are usually installed up high and have vents on underside too, so that would have to be taken into consideration if you went this route.

http://www.vintagemeetsglam.com/2015/10/05/bedroom-makeover-part-6-diy-ac-unit-cover/

a really good scrub, let dry, then prime with ESP outside. When dry, paint of your choice.

A local car panel shop paint plastics all the time. Bumpers bars, grilles, interior parts, etc. so they could paint it for you. They'd use the correct plastic primers as well.