Is there a coolant pressure specification for Ophir water-cooled sensors?

Yes. Please reference the chart below:

Minimum Flow Rates for Water-Cooled Sensors

Sensor Recommended flow rate at full power1 Minimum flow rate at full power1 Absolute minimum flow rate pressure drop across sensor (at maximum flow rate) pressure drop across 8 meter of tubing (at maximum flow rate)
liters/min) (liters/min) (liters/min) Bar MPa Bar MPa
L250W 3 3 3 0.3 0.03    
L300W 3 3 3 0.3 0.03    
1000W 6 3 3 0.3 0.03 0.5 0.05
L1500W 6 3.5 3 0.3 0.03 0.5 0.05
L2000W 6 3.5 3 0.6 0.06 0.5 0.05
5000W 8 5 3 0.6 0.06 0.5 0.05
6K-W-200x200 6 6 5 0.5 0.05 0.3 0.03
10K-W 8 8 3 1 0.1 0.5 0.05
15K-W 12 12 3 2 0.2 1 0.1
16K-W 12 12 3 1 0.1 0.8 0.08
30K-W 25 25 6 2 0.2 3 0.3
120K-W 60 60 30 4 0.4 3.5 0.035

You can find a lot more information about the correct use of water-cooled sensors in the article "How to use water cooled Ophir sensors", here.