Are you talking about 30" short scale, or something like 32"?
For Drop C (CGCF) at 32", it is possible to play with something like .055 to .115 if you don't mind lower tension. I use this setup often myself for a 32" bass that I use for Drop C but often tune the low C back up to D. You *might* also be able to go up to E flat in this setup. If you want standard tension you'll want to go a little higher, but then you're unlikely to be able to go up to E flat easily.
If you want to play Drop C on a 30" scale bass you're likely going to want to go .125+ for the low string -- basically grabbing the low-B string from a typical five-string set. I personally was not a fan of this type of setup but it is an option. I don't think you would be going back and forth between tunings with this setup though.