Make it so that the manufacturing cost of a $100 bill is $100 minus the amount you want the counterfeiter to make, so for $1 say $99. Include tons of security features, use silk, gold, diamond dust, whatever. Then just let the market do it's thing.
Have money testing machines that shred fake bank notes at sight. You may or may not want to keep punishments for using fake bank notes. You just want to keep a little bit of pressure to keep the manufacturing costs so high that you control monetary supply. (Now that I think about it, supply of bank notes != monetary supply. You'd have to physically print A LOT to shift the value of a currency notably.)
There are a ton of reasons why this wouldn't work or wouldn't be a good idea. For one, a complete waste of resources. Also, you wouldn't have as much control over the money supply. And advances in technology change the production rate and profits from printing rapidly.
All of those caveats also apply to Bitcoin, of course.