there is a B&B that does monthly and weekly rent in Rio. It's called Pousada Casa 14. The guy who runs it is a writer/translator and speaks good English, French and some German. The house is very beautiful and in the heart of rainforest in Floresta da Tijuca. Great for walks. It is very convenient to the city centre and not very experiense compared to Ipanema, Leblon or Copacabana.
Have a look at their website http://www.pousadacasa14.com.br/ I hope that helps..