Thanks for the helpful replies and link. I went to our local Menards to check out their offerings. I wound up buying a Surebonder Triggerfire. Looking the packaging over, it appears to be part #5625, although they make you hunt for that information. I bought a pack of Surebonder #4 1/4" heavy duty staples, part # 55014. The 1/4" refers to the "depth" of the staple - how deep it goes into the wood. 1/4" is plenty. The packaging on the stapler says "Perfect for upholstery," so I figured (really, hoped) the hardwood used for furniture would be similar to my Williams playfield.
The stapler drove the staple to a perfectly flush position with the playfield underside - it had a perfect amount of force. The staples are a good likeness for those originally used on my 1955 Williams King of Swat. The packaging says "Narrow Crown," which I believe is the visible part of the staple. I'd get a wide crown if I had the option, but the narrow crown is perfectly satisfactory, in my view. Overall, I'm delighted with the Surebonder. The only downside was mentioned by ForceFlow - ideally, you've got to lay the 7" stapler flush against the playfield before firing the staple. I was working on a Williams pitch and bat game, and they are pretty sparsely populated compared with a pinball of the same vintage. You can cheat a little bit by driving the staple in at an angle.