Treating the ceiling is your best bet, as already mentioned carpet doesn't actually do much for most frequencies. One option is just covering the entire ceiling in fabric-wrapped acoustic panels, but your better bet is finding a local acoustic consultant who can do a quick RT60 test of the room, and recommend an exact sq. footage of treatment (most likely, their total fee will be less than what you'll save by just treating the entire ceiling).
Buying Owens Corning fiberglass panels and wrapping it yourself was mentioned, which is possible, however I've seen this attempted a few times and it rarely looks good. Buying pre-wrapped fabric panels from an acoustic company (e.g. Kinetics, Decoustics, MBI, Armstrong, etc.) is nearly always a better way to go so you get a decent looking end product.