Somewhere around here I posted a thread called "The definitive 4-way vertical list". I listed all the originals that had a 4-way and a vertical screen. I didn't just use the bad info in Mame either. I actually checked each and every vertical game in mame to see if it was a 4-way game or an 8-way game (there are so many listed wrong it isn't even funny, and my list also included 2-way games, which normally only show up on 8-way lists).
I believe I went up to 3 buttons with that one though. Most games were one button, most of the rest were two, and only a few were three. A second button might really help you out.