By removing
The two stones in the third column
We can generate the following uniquely solvable solution

Reasoning
The three stones in the top left-hand corner are incompatible, hence one of them must be removed. Similarly, the stones in the bottom left-hand corner are incompatible, hence one of these must be removed. Developing the right hand side of the grid leads to the following.

From here, if the black stone in the third column remains, there must be a line emanating from it going up. Similarly, if the black stone in the second column remains, there must be a line emanating from it going right. These endpoints will necessarily need to be joined up and there will always be at least two ways to do this (thanks to jafe for pointing this out).
Hence, to get a unique solution, at least one of these black stones must be removed.
From there, there are just five combinations of stone removals to test for existence of a unique solution.