The copper pipe and tray idea was what I was going to suggest. Put a lid on the tray that covers the back half so when you pull it forward, the tokens are blocked from falling, and you'll always get a set number (maybe, I could still see things jamming).
I wonder if an antique gumball machine could work, you may have to drill out or otherwise enlarge the ball opening on the inside, and you'll likely get more than 4 tokens at a time, but there may be a way to avoid that even...