I want to do an appearing bowling ball but want to paint it to fit a theme. What type of paint would work where I wouldn't have to do a touch up every time...?

If it were me, I'd investigate KRYLON FUSION FOR PLASTIC aerosol paint. It is described as flake and chip resistant due to it's characteristic of bonding with the surface to be painted. Your mileage may vary.

Cheers!

Thanks!

Sand the surface first with 220 then clean it off.

Yes that KRYLON infusion spray paint will work and works very well if you cannot find the color or coloring you like in that line there is a spray on plastic primer that will make a surface useful to allow paint stick and not flake off. Same place you will find all the other spray paint.

I need it mostly white, so that primer might do the trick

Primer alone is usually porous. It’s very function is to be a go between,
Just sand it then spray light coats of the Krylon by arching your hand and arm to conform to the spherical shape
If you just arc back and forth then you probably get a sag,
6 light coats are better the two heavy coats

Give it 8 hours between rotating the ball and reciting

If you wanted to get fancy… You could put an expandable plug in one of the holes and attach a line to a pulley, hanging the ball, then you can spray the entire ball in one sitting by raising or lowering it through the process… but you still have to do light coats.