Good morning, are there places to rent a bicycle in Copacabana?
Try Via Pedal... (see google). have good experiences with them. They also have some cool group events a few times per month
There's a list of places here: http://riodejaneiro.angloinfo.com/af/269/Bike-Hire-Scooter-Cycle-Rental.html
Via Pedal is one of them. As Canger said... they are good :)