The HTML entity for the Turkish Lira works in all web browsers but Prince outputs ?837 in its place. Can this be fixed? The code is ₺.

Which operating system are you running Prince on?

On Linux the DejaVu fonts have glyphs for Turkish Lira, but the Microsoft Core Fonts do not.

I tested it on my Macbook, our server is CentOS. Where can I get that font for those two OS's?

On CentOS 6 you can install the "dejavu-serif-fonts" and "dejavu-sans-fonts" packages.
I will need to check which fonts are available with this glyph on MacOS X.