Picking the right cap is part voodoo, part conventional wisdom for debouncing via noise suppression.
Voltage isn't important. Just pick a cap rated to (typically) 25-33% higher then your operating voltage. This is just headroom over-speccing.
Value is handled by our friend the RC Time Constant.
"But WD!" you'll say. "That takes a pullup resistor!"
Then I remind you that the input is either internally pulled up (90's and onwards) or has a pullup at the board.
http://www.ganssle.com/debouncing-pt2.htmMath is there. Here's the short of it: Most switch bounce lasts less then 10-20msec. Most debounce caps you'll ever see are 0.1 or 1uF.
Larger caps put a big honking delay on the line, which can cause the board to ignore a coin drop that's quick behind the last one.
My guess is that's why that cap is there. That, or that cab's original board had some serious gremlins.