I stand corrected... just slightly
This website says it was used from 1948 - 59. Click the link below...
http://www.sportslogos.net/logos/list_by_team/71
I think it's more of a guideline than solid fact. It says the cartoonish Pirate was used 1960 through '67, but I think they were actually done with that one by 1964 or so. If you need to pinpoint it further, the best way to determine would be to reference Pirates Yearbooks, Scorecards and other periodicals.