How can you determine the year a Winchester Cooey Model 750 rifle was produced?

your Winchester mod 750 is probably a 1964,that is when they bought cooey and made the most .22's

The Olin Company ( Winchester) took over in 1961. If it has no serial numbers, it would have been made between 1961 and 1968 when serials were required on each gun.

Cooey made the most different models before 1961..at least 29 recorded models