There is VASP, but this airlines is not reliable and tend to cancelled their flights easily for no reasons.
I was waiting in Rio Santos Dumont Airport for a flight with VASP to Sao Paulo. My flight was cancelled so the one following.
I was advice by used travellers between Sao Paulo and Rio to get a ticket for the airline GOL, it was a good price and the flight was fine with a new aircraft in which I felt perfectly safe.
So I will advise you to take a GOL flight, you can buy ticket there just before flying as it is cheaper.
Info about schedules:
http://www.infraero.gov.br/sivnet/modelo.php?ai=SBRJ