What is the value of a Liberty head silver dollar 1989 Carson City?

I assume you mean 1889 !

If that is what you have, you will need to have it authenticated by a certified dealer or appraiser, because a genuine 1889-CC Morgan dollar retails at $450 to $4000 depending on condition. However, over the last couple of decades there has been a flood of counterfeit Morgans made mostly in the Far East, so be prepared for the possibility that your coin is one of those.