The boat left the remote town of Oron, in Cross Rivers state, on Friday and was heading across the Gulf of Guinea to Gabon, in central Africa, when it capsized.
A doctor at a hospital in the coastal town of Calabar said they had received 45 bodies of passengers who had drowned.
David Akate, head of Cross Rivers emergency services, said he had no official death toll yet.
Two known survivors were a young boy and a woman who had clung to a gas cylinder and were rescued by fishermen.
Yushua Shuaib, spokesman for the National Emergency Management Agency, said they could only confirm nine dead so far.
Boat accidents are relatively common in Africa, where safety standards are poor.
As many as 138 people died when an overloaded boat carrying passengers and goods capsized in rough water on a river in Democratic Republic of Congo in 2010.
Some 35 people taking this route from Nigeria to Gabon died after their boat sunk off the coast of Cameroon in 2008.
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