Simple solution, offer money.
rarely do people donate sperm or eggs or even blood out of good will, and those (mostly the former) are relatively freeflowing and without risk. You usually have to coerce somebody to do it. The same will apply to Kidneys. Personally, I'm rather fond of both of my Kidneys, I even have names for them (not really.) To rip one out? Maybe you should be greasing the gears a bit by offering cash and a cup of orange juice for those that donate a kidney.
Another easier solution, is the wonderful cure all magic gel that is Stem Cells. We could repair kidneys, hopefully fixing the problem or atleast prolonging the person long enough till a transplant is available. Or with even more advanced stem cell research, we could actually GROW a new kidney, in a lab.