Just curious, why do you wanna tune to CGCF? Not very many bands use that tuning....unless you are trying to learn some early mudvayne or something. Unless you have a 35inch scale bass and some heavy arse strings, its going to be really floppy. I play a 34 inch scale with heavy set strings. I tune to C# though.... But after I tune to C# I drop the top string bout half a step. Then again, my band is really heavy and low. I find the easiest way to get this tuning though is without a tuner, or with little use of a tuner. I use my tuner to tune to EADG, then I play a C note and tune my top string to that note....After that its alll tuning by ear and is pretty simple.
I may be wrong about this...my bass skills arnt the best, but thats how I tune to the lowness you desire.