The opposite cycleways (road that you can cycle in the opposite direction of other traffic without a dedicated lane) with the tag cycleway=opposite (as described in OSM wiki : http://wiki.openstreetmap.org/wiki/Cycleway)) are not rendered on any rendering project (OpenCycleMap, Mapnik, Osmarender,…)
This kind of streets are very common in Belgium, but we don’t have maps to see them.
cycleway=opposite does not show an opposite cycleway, but a road that one is allowed to go ‘against the one way’ by bicycle, without a separate cycleway for the purpose. If there is a separate opposite-direction cycleway, one should use cycleway=opposite_track or draw a separate way. If there is a single way, but with a separate lane for cyclists going the other direction, one can use cycleway=opposite_lane.
These are by the way all rendered on Osmarender: If cyclists are allowed against the one-way traffic, the arrow for the one-way traffic is solid green, if they are not it is white with a green border. It also shows cycleway=lane and cycleway=track (as well as opposite_lane and opposite_track) by a green border on the road. Unfortunately the same does not hold for the cyclemap, which does recognize cycleway=lane, but not cycleway=track.