If no one checks by the time I am home I will try to remember to check mine.

From the parts list on IPDB:

1400 .2 A-18147 coin toss exit assy 1
1401 ..3 01-12592 brkt-toss exit 1
1402 ..3 07-6688-18N rivet 3/16X1/8 nickel 2
1403 ..3 31-1925-27 plfd plastic-world cup 1

Looks like it was originally riveted.

Correct, it should be riveted.

Riveted from the factory.

I'm currently replacing ramps on a White Water, and I intend to use screws to replace rivets. Does anyone have any recommendations about what kinds of screws to use? Does anyone think this is blasphemous?

Why not just replace the rivets? Not too hard to do.

What's your riveting tool of choice?

A simple punch tool. Very easy to damage plastics with though. I hear these work well. http://www.pinbits.com/index.php?main_page=product_info&products_id=72
You could also build your own press with this http://www.harborfreight.com/1-2-half-ton-arbor-press-3551.html
http://www.pinrestore.com/Riveting.html