Ok, so there was never a Federation carrier on-screen (TOS aside; I've only watched some episodes a friend of mine hand-picked as 'the best', and read some of the TOS novels). Yes, the Akira was supposed to have fighter decks, AND be an awesome torpedo boat AND have the rear torpedo bay-pod-thing rotate 360 degrees to fire in any direction. However, since on-screen generally = canon, we haven't seen a carrier yet, in that sense.
The first objection I always hear to a Federation carrier is the concern for life. Let's face it, fighters and fighter-bombers succeed primarily through strength in numbers in Star Trek; unlike Star Wars, the fighters can't be too fast for the turbolaser batteries, etc. Sure, they can dodge some shots, but not indefinitely.
Enter the unmanned combat/utility drones. If the Federation ever deployed a carrier in this timeframe, I imagine they would use some sort of unmanned fighters (drones), so as to minimize the risk to the life of the ship's crew. The automation systems would be directed by link to a command/control computer on your ship, which tells them which targets to attack. As EDI would say, the CIC determines who to shoot, and the drones would determine how to shoot.
I realize that Federation fighters themselves have made appearances on the screen, both in DS9 and in Insurrection. I also realize that most people (myself included) will want to see the Peregrine, etc., appear in-game as carrier-based fighter craft. I can't picture it being impossible for the Federation to adapt existing craft (rather than producing new ones) to this purpose, given the ongoing war, though.
This may have already been proposed, and I simply failed to find it in a brief search, but I thought this may be one way to get the ball rolling on a Fed carrier (although this would, understandably, be some time in the future, unless Cryptic used the Jupiter as a carrier, or had another design lying about).
I'm not 100% sure of it myself, but it may help...what do you guys think?