E-bikes allow for longer and easier rides even for untrained cyclists, but the riders can take full advantage of their bikes on cycleway networks that are equipped with Charging Stations (CSs) for extended autonomy. Therefore, CSs must be deployed on a cycleway network so that a bicycle rider can find a CS before running out of charge, though budget constraints limit the number of CS that can be installed. In cycleway networks structured as simple paths, we prove that the problem of deciding where to install CSs in a uniform way and complying with budget constraints can be mathematically formulated and solved very efficiently with an elegant algorithm supported by a graph representation of the problem. The approach will be extended to linear cycleways having alternative branches. The more general case of a cycleway network is studied. This case requires a more complex discrete optimization model, and alternative approaches will be discussed. The models will be applied to a set of cycleway networks with different shapes.