After some searching on the net, it seems that Apple has somewhat broken the way that it deals with Linux CUPS shares. Apparently it only searches for printers via Bounjour. In any case, I found a fix that works perfectly. Alessandro Dellavedova posted a fix for the problem over on the Apple support forums. Below is a slightly more detailed version of what he did.

WARNING: You will need administrator privileges to proceed with this fix.

1. Open System Preferences.
2. Open Print & Fax.
3. Right-click in the printer’s pane and select “Reset printing system…”
4. Open Terminal and type the following:

   sudo nano /etc/cups/cupsd.conf

5. Modify the first few lines such that they look similar to the following:

   Browsing On
   BrowseOrder allow,deny
   BrowseAllow all
   BrowseProtocols all
   BrowseRemoteProtocols all
   BrowsePoll <Your CUPS Server domain or IP>:631
   BrowsePort 631

6. Save the file
7. Restart the printing subsystem by typing in the following:

   sudo killall -HUP cupsd

Now you should be able to see and add the printers on your Linux share.