I made about 10 million per hour today just scanning plants, that's quite a low per hour rate compared to some other activities but I was having a restful day. In two hours I earnt enough to keep the carrier running all services for a week, and over the afternoon I earnt enough to run it for a month.
To be honest once you get above a certain number of credits, they largely seem to roll in in huge numbers without much effort - most Commanders who own FCs seem to find this, I think. There are huge payout missions which don't take too long, as well, once you have decent ships. You will need about 7 billion to buy and fit out a carrier satisfactorily though, unless you want it "bare bones". Then again with a Federal Corvette costing the best part of a billion to fit out decently the FC is a bargain.