Is there a particular reason you want to find a fork without an air spring? Coil spring forks are getting more and more difficult to find. Plus, most manufacturers only offer 3-4 different spring rates which can make it difficult to find something that will work for a Clyde.
Looks like the RockShox Dart forks offer both coil springs and rim brake support. There are several other RockShox forks that feature coil springs, but most require disc brakes.