Calibrating Correlation
First what comes to my mind: "the only statistics you can trust are the ones you have falsified yourself" - Churchill

However, to answer your question.

The correlation coefficient is defined as:



You can find data points that are negatively correlated by looking at the covariance, that is defined as:

 

First, you calculate the mean of your dependent and independent variable. Then you subtract the mean from the corresponding data points. After that, you multiply those two series. Negative values are rows that contribute to a negative correlation coefficient. 

However, as a statistician, I am not supporting this approach (data deletion on purpose is not scientific working).