Many (most?) ground-based telescopes are funded by private donors: e.g., the Keck Telescopes, the Allan Telescope Array, etc. Space missions, not so much. My guesses for why: the costs are significantly higher, and NASA isn't set up bureaucratically to work with private capital.
That said, private money for technology development efforts or data analysis could likely be well-used.
That said, private money for technology development efforts or data analysis could likely be well-used.