1] scuff the plastic with a fine grit paper or some 00 steel wool.

2]  Get any primer, chances are a grey primer best for your silver
match. Krylon works fine.

3]  Two coats of primer, allow each coat to dry before next coat.  Then
scuff the primer coats with very fine paper, use the wet-sanding
technique.

4] Allow to dry, NOTE~~~~~~~mask off the glass and surrounding areas
prior to doing any of this.

5]  U need heat for the paint application to bond to the primer.
Krylon plastic primer and paint, sold at all K-Marts and Wal-Mart's
does a good job.

6] Apply the paint in several coats, do not try to cover in ONE
coat!!!!!!!!!  Allow each coat to dry before apllying next coat.  Take
your time, it does not happen instantly for a good DIY job.

7]  Ensure you have some heat at each primer or paint application,
either sunlight and some decent ambient temp. [at least 70 degrees or
more], or use a hairdryer on low setting, and let each coat dry for say
one hour.

The only hassle I can think of is getting the silver color to match the
ride's color, that is first in the paint color, and then by your visual
as you apply paint coats.

yeah, an enamel most likely much better than a laquer.  He could get the
matching color spray paint OEM dealer, but that'll run a bit more $$,
sigh.

I did forget to suggest apply a good clearcoat finish once it's all
said and painted.

Being it is a 2003 I would HIGHLY recommend having a body shop do the
painting, That way you don't have to worry about all the problems.

However if you want to DIY.

The catch to a DIY paint job is going to be matching the color and
metallic type. I would go to a body supply store or another place that
can do a custom mix. Or order a factory pack through a dealer. You MIGHT
get lucky and find a Dupli Color match. You will need a primer a base
color coat and a clear coat. Make sure that all of them are compatible
types. Mixing materials can almost guarantee a failure unless you KNOW
they work together.

As for prep.
Wash the housing with a GOOD detergent, this will remove any dirt or a
mold release agent if it is new. Now put on a pair of rubber gloves.
Wipe it down with a wax and grease remover. Now use some 200 grit paper
and a random orbit sander to sand the entire surface, pay attention to
the edges and the interior as well. Now use a tack cloth to remove the
sanding dust.
Use some LIGHT GRAY primer and spray on three light coats, letting each
coat tack up between coats. Let it dry and scuff the primer coat with
some 320-400 grit. Now for the fun part. Hang the housing so it is in
the same position as it would be when installed on the car. Use a tack
rag and dust it clean.

Read the directions on the paint regarding color/clear topcoat time.
Some you can clear as soon as they flash off the solvents and some you
need to wait an hour or more.

Now spray on two - three LIGHT coats of color, ANY runs, dirt or bug
crap and you get to start over by sanding back to the primer. If you are
using a Base/Clear system the color coat may not (usually is not) be
glossy. Once you get the color on without a problem  DO NOT TOUCH THE
HOUSING.

Wait the proper time and spray on 3-4 coats of clear with time enough
between coats for it to flash the solvents away (read the instructions
about flash time).

I went with these guys: <https://www.paintscratch.com/>
Aside from the primer, color, and clearcoat (which you might not need)
I got the adhesion promoter which is supposed to help the paint stick
to plastics. I also got the sandpaper, wax and grease remover, and
rubbing compound from them, just for simplicity but you could probably
shop around.