I just flew a dog back from Benin, and it wasn't cheap; something like $1,500 all told. The requirements will vary depending on where you're flying through — your layover is just as important to consider as your final destination in the U.S. http://www.pettravel.com
is a good site with lots of information about various airlines, their policies, etc.
But here was my experience: To get form Benin to the U.S., you can transit through Morocco, Turkey, Ethiopia, France, or Belgium. Of these, France requires your pet to have had a blood titer test several weeks before travel (I forget how many); the test proves that the pet has been vaccinated for rabies. Belgium does not, nor does Turkey. My wife and I never really considered Ethiopia or Morocco because the layovers were too long, and we did n't want our dog to be stuck in the airport so long. We were originally to fly through Belgium, but the attacks there stymied our travel plans, and we eventually got rebooked on Turkish Airlines.
If you have time to get the titer test, you should be fine with whatever airline you choose and whatever layover destination you choose. As far as I know, the test just requires a vial of blood to be drawn, but they may have to fly the blood to Europe for analysis if there's no lab in Ghana that can do it. If you opt not to do the test, you have to be sure to fly through a country that doesn't require the titer test. If you go through a country like France anyway without the titer test, they will force you to see a vet in France and board the dog for the several weeks it takes to get the results back!
Then you need to decide whether to go directly through the airline or to go with a cargo service. You might consider a cargo service, since you'll pay either by weight or by volume, and for a cat, this may cost less than paying the airline directly. The cargo company will also handle the red tape and paperwork for you to the extent possible. Ask your airline what local cargo companies they deal with, and then contact them for their policies and rates.
Expect to be asked to microchip your pet (vets in Accra should be able to do this) and to get a veterinary exam a few days before departure.
One final thought: It's not easy flying a pet home, and the particulars for your country may be different form Benin. Ask around among the Peace Corps, embassy, and broader expat communities there for help. Someone is bound to have gone through this. (I benefitted from several other volunteers who had left before me with dogs.)
[Edit: Just realized the original post was two years old! But hopefully this'll help people down the road...]