I'm in a Computer Science class that is constructing a "C-" compiler,
which is a small subset of the C language that does not have structs,
pointers, etc. It's pretty simple, with a grammar of 30 rules or so.

I'm looking for resources that will help me implement Design Patterns
and Object-Oriented concepts for this. (I'm writing the compiler in
Java, although C# is also acceptable, I believe) The textbook I'm
using has numerous examples in C, so it's a bit
antiquated in some ways, because I prefer an OO approach to
programming. I'm pretty much on my own besides that, the class teaches
functionality, not implementation.

I have the "Design Patterns" book by the "Gang of Four", and it's a
good start, but things like the "Interpreter" pattern don't seem to
scale well to large grammars. I could be wrong, however. So I'd like
ideas on what books to buy or websites to visit that would help me
implement my compiler in a OO way w/ Design Patterns. I'll tip
pleasantly for good efforts :)

(note: if you feel the price for this research is too low, let me know
and I'll increase it.)

I would suggest the following books (listed in no particular order) if
you haven't already:

Writing Compilers and Interpreters by Ronald Mak
Modern Compiler Implementation in Java by Andrew W. Appel
Programming Language Processors in Java: Compilers and Interpreters by
David A. Watt and Deryck Brown
Building Parsers With Java by Steven John Metsker

Also take a look at the source code for JavaCC
(https://javacc.dev.java.net/) and SableCC
(http://sablecc.org/index.html).

If it is a C- syntax, is it a requirement for you to write this from scratch?
Flex and Yacc tools on unix and windows have been there for a long
time and can do the work effortlessly.

All you would need is a shell over this in C# to handle the input and
outputs -You can keep that object oriented while the core work is done
in C -

Tell me if you are intrested in this idea -

Yes, it has to be written from scratch :)