On board color profile.

[lew1716]

Is there a way to tune the raw file colors? In general, shots taken in direct sun are too saturated in the reds and greens, and instead of looking like a flat raw file, the colors are far more saturated than they appeared in reality.

[Cameratose]

No, RAW is RAW. Gerald Undone did a test and determined the only setting in the picture profiles that can affect RAW is Gamma. See link below.

How are you viewing the RAW files? They can look different depending on your processing software. 

YES, Sony Picture Profiles DO Change Raw Photos! (geraldundone.com)

[lew1716]

I'm looking at the LrC previews. They pretty much match my printer output, so it isn't something quirky about the display.

[Pieter]

RAW images don't have a color profile or saturation setting. It's the default profile used by your RAW viewer/editor which determines what your RAW files look like when viewing them. Try using a different preset.