Op amp diode clipping
You can add a series resistor between the op-amp output and the diodes to limit the current. Something like 470 ohms will limit the current to less than 10mA. Take the feedback from the output rather than across the diodes or the op-amp will saturate when the diodes conduct. 

The short circuit current of the op-amp ADA4177 is typically almost 50mA and can therefore be considerably more in specific cases.