I haven't found a map of it, but here is a proposal from the early 1960s of a partition of Cyprus:
After this plan was rejected, a second was also discussed, but it was not taken seriously.
https://hellenicantidote.blogspot.com/2009/07/acheson-plan-for-partition-of-cyprus.html
Based on what was written there this is my best guess as to what it would look like using this as the base map. I found a Peristeria seasonal river that runs south of the Kyrenia range so I assumed the Peristeria they are referring to is somewhere north of that. The Turkish Sovereign Base Area is shown in Green (with the monastery area at the tip of the peninsula excluded). Everything in yellow and purple outside of the Sovereign Base Areas (green and red - for Turkish and British) would become part of Greece). Also shown are the Turkish enclaves of around 1973 (which I assume are a good proxy for the Turkish areas in 1963-1964) and the lines reached by the Turkish Army on July 22 (Orange - first offensive), August 8 (brown, prior to the second offensive) and August 16 (pink, after second offensive) in 1974:
I also found reference to other partition plans in the 1960s:
This one (from the first link) is actually close to what actually happened and roughly to the Acheson Plan I think: