Quoted from Freeplay40:

The type of rivets used on pinball machines are called Oval Head, Semi-Tubular rivets. Primarily all the rivets are 1/8" in diameter (shaft). The trick is the length of the rivet needed. Basically when you assemble what you are riveting, the semi-tubular end will protrude about 1/8" beyond the bracket or the washer if needed. Most common lengths for flaps and brackets are 7/32" and 1/4 inch. Whenever the rolled over end of the rivet would be against plastic (look under one of your flaps) you must use a washer.
Pin Restore sells a great rivet starter kit which I would highly recommend for $30...see link...
http://pinrestore.com/Riveting.html
His kit contains nickel plated brass rivets. Brass rivets are easier to "roll over". I use all steel nickel or zinc plate rivets. That kit and the hand held roll over tool from Hanson Rivets (Item HT-174) is really all you need to do most riveting... A press is also handy but cannot get to all rivets. The hand held tool can do everything. You just need to solidly support the head of the rivet while you hammer the other end. For brass rivets a piece of hardwood works well. When I use the hand held, I either position the piece in my vise or use a bolt that I have ground concave to match the rivet head, again in my vice.
Here is short video I did here on Pinside demonstrating the hand held roll over die.
https://pinside.com/pinball/forum/topic/swords-of-fury-custom-ramps/page/8