There is a cycle-oriented OpenStreetMap render available, called OpenCycleMap. Sadly, OpenCycleMap is not really open (as in opensource) and it is not easy to report issues and get bug fixes. Moreover, you cannot selfhost it and have to pay after a given number of requests.
There were discussions recently, on
#email@example.com and on the
about eventually having an alternative render dedicated to cycling which would
be totally opensource, free software and selfhostable.