Good news: no need for laminate!
I used 'Varathane Colors in Plastic - Black Satin' paint and it looks amazing - just like laminate! The only problem I had with it is that the surface you're painting does have to be completely smooth, or it does show. There were a couple of areas I didn't sand down completely smooth and they did stick out.
Also, on a recommendation from one of the example sites (Sorry, can't remember which one), I used the 'rustoleum Semi Gloss Black Hammer Finish' paint on the coin box, and that also did an amazing job. The hammer finish covers up any defects and makes it look like new!