A long time ago...
Bruce Thom (BAT) made a falling block single shot action. I think that's how he got his start in the action business. Good luck on finding one.
More recently Alan Hall made a few. Ditto on finding one.
I have collected and shot falling block single shots for many years. To me the best by far is the Ruger No. 1. First, it's good looking. It's very strong. There are a lot of them and you can find one easily. Best, I think, is that there are gunsmiths out there who know how to make one that will shoot accurately.
My deer rifle is a small No. 1 made in the late 60's. It has a four digit serial number. It has been completely customized with lots of stock and metal work and engraving. I put a Kepplinger set trigger from Brownell's in it a couple of years ago. The trigger breaks at a very crisp 4 lb. when not set. It breaks at a crisp 1/2 lb. when set. It shoots very well in spite of having the original barrel. The result is a small, light rifle which handles very well, shoots accurately and is fun to just look at.
If I wanted a new varmint rifle I would make it from a No. 1. It would be bigger and heavier than my gun, would be chambered for a sensible varmint cartridge and would probably have a Unertl scope thereupon, just cause.
Dick Wright