I have personnally operated centerless grinders and ground tens of thousands of tungsten carbide parts.  Water based products are preferred to move the heat you generate when grinding.  Staining on the parts usually means leaching of the cobalt, and that's a major concern.  You are grinding tungsten carbide  because it will be used in a hostile environment that will test the strentgh and wear resistance of the material.  It can't be compromised.  

Oelheld U.S. has just introduced a new addition to its poppular water based lubrication line.  According to Oelheld, AquaTec 5001 is a high performance, synthetic metalworking fluid specifically designed for moderate work on cemented carbides. The oil free AquaTec 5001 contains a highly effective combination of inhibitors that significantly reduces leaching of cobalt and nickel binders. AquaTec 5001 also provides excellent lubricity and cooling for extended grinding wheel life, and superior work piece finish. Grinding wheels remain open, and swarf quickly settles to the sump for easy filtration.  AquaTec 5001 can be used in “stand-alone” machines and central systems. It is an ideal product for grinding applications such as surface, center-less, ID, OD, and Blanchard - grinding, and can also be used for light to moderate machining duty.  AquaTec 5001 is extremely low foaming, making it an excellent choice in high-pressure applications.