It is possible to make spaces alcohol-free without creating a liquor/alcohol ban or Alcohol Control Bylaw.
Obviously restrictions that are not in a policy or bylaw would not be enforceable by the regulatory authorities. However, the owners of the spaces can still ask that no alcohol is brought into or consumed in the space.
Contact the owners or other people/members responsible for the space and ask them if they have considered making it an alcohol-free area. If you have any evidence of alcohol-related issues take this with you.
If you are a member of a club or group that uses a space put a motion to the committee or group members.
If it is a Council-managed space/venue, ask to address a community safety or similar committee and make a proposal to them.
Seek support from others prior to doing this so that you can demonstrate that this is something that would be valued.