Library>Fonts takes priority over ~username>Library>Fonts.
Think of it this way. Library>Fonts, available to all users. ~username>Library>Fonts available to that user only.
OS9 Classic fonts are at the bottom of the hierarchy. Consequently, if you have say Helvetica in the Library>Fonts, OSX is going to use that Helvetica over any Helvetica stored in the OS9 System>Fonts folder. The one exception to this is if you start Classic and use those fonts IN Classic apps.
So.. The only course of action you have is to remove the font that is in the Library>Fonts folder and replace it with the one in the Classic folder. Now, here is where this get's messy. If the font you need to pull out of there is a font that the OS relies on and you are running Leopard then Leopard is going to automatically replace the font you just pulled out — unless you tell it not to. If it's not a font the OS relies on then it should not be an issue. To tell Leopard to stop replacing system fonts, open FontBook and uncheck these preferences: Automatic Font Activation and Alert Me If System Fonts Change.
Have a look here. This is a handy guide that will show you exactly which fonts you HAVE to keep in the various font folders. Again, if the one you are having issues with isn't on the required list than you can just replace it with the one from the Classic folder. Follow the guide if what you need to do is remove Helvetica or Courier!
That SHOULD take care of it. If it does not, we may need to purge font caches (which is not half as scary, or dangerous, as it may sound, and easy to do).
Hope some of that helps.