There really are no good spots to anchor at Cooper. You could go around the point to Carvel bay and dinghy back around. Stopping to swap tanks and have lunch at the Cooper Island Beach club was something we used to do all the time. Sadly with the advent of Boaty Ball it’s much more difficult so we skip it. Cooper tends to be most crowded Saturday-Monday. I think you will be able to find a FCFS ball on other days of the week for lunch until more balls get converted to boatyball.
G