Cllr Coyne cited the reported difficulty raised by some car drivers in understanding where 30mph and 40mph limits are in force and that a uniform urban speed limit would simplify that issue.
He also wants the council to make sure that existing cycle routes, such as the one alongside Speke Boulevard, are regularly swept to remove broken glass that can make them hazardous for pedal cyclists to use.
At the council meeting tomorrow, Cllr Coyne will be calling on Cllr Peter Millea, the executive member for Regeneration and Transport, to appraise the ideas he has raised to make life easier for cyclists, as a way of encouraging more green transport.
Cllr Millea is being asked to compile a report to the relevant select committee so that the measures outlined by Cllr Coyne can be considered.
Liverpool has carried out a programme of providing cycling lanes, but cyclists complain that they are usually narrow strips of road, often ignored by motorists.
Cllr Peter Millea, the council's regeneration executive member, said: "I would support reductions from 70mph to 40 and from 40mph to 30 wherever possible. Cycleways are not always possible to implement on existing highways, but we do try to include them in new-build roads.