When trying to convince Mordin to lie to the Krogran about the Genophage (so he doesn't die ), I find that the dialog choices to convince him are blanked out. How do I unlock them? Do I require a certain paragon/renegade rating?
By blanked out, do you mean you see them on the left hand side of the wheel, but in grey?
If so, it means that yes, your Paragon or Renegade score isn't high enough.
Dialog on the top left/bottom left corner of the wheel occasionally shows up in Blue, Red, or Grey. Blue on the top Left is a Charm dialog, and often requires a minimum Paragon score. Red on the bottom left is Intimidate dialog, and generally has a minimum renegade score. Charm/Intimidate options for which you don't have sufficient reputation are shown in grey, because you cannot select them.
In the case of the Genophage cure, if you are in a position to convince Mordin to lie (which is a complicated set of circumstances all it's own), then either the Paragon or Renegade option will work.