How can I make a Pink Noise generator?

Pink noise is just white noise put through a -3dB/octave LPF. You can generate white noise using rand() (or any function that generates uniformly random numbers).

Streaming stuff to the soundcard is reasonably trivial, as long as you have Google handy. If you choose to avoid DirectX, consider using PortAudio or ASIO for interfacing with the soundcard... although I think you're gonna have to use C++ or C.

Other than that, why waste CPU time generating it? Loop a damn WAV file!

bit late to this i realise, but anyone coming across it for answers should know that pink noise is white noise with -3dB/octave, not -6 as stated above, which is actually brown noise.

Maybe you can convert the C/C++ code here to C#:

http://www.firstpr.com.au/dsp/pink-noise/

The easiest way to get sound to the sound card is to generate a wav (spit out some hardcoded headers and then sample data). Then you can play the .wav file.