For my travel I rented a bike from this rental shop.
Megasport Algarve rents a wide range of bikes, offers a bike delivery/collection service for free in the whole region, organizes also guided and self-guided tours of the Ciclovia. Definitely recommended!
Bike shops and mechanics
Here you can find an updated list of bike shops in Portugal: https://pedalportugal.com/directory-links/bike-shops-mechanics/