to have a good time ( = a time of enjoyment) was common in Eng. from c 1520 to c 1688; it was app. retained in America, whence readopted in Britain in 19th c. [OED]
Time of day (now mainly preserved in negation, i.e. what someone won't give you if he doesn't like you) was a popular 17c. salutation (e.g. "Good time of day vnto your Royall Grace," "Richard III," I.iii.18). Times as the name of a newspaper dates from 1788. Time warp first attested 1954; time capsule first recorded 1938, in reference to New York World's Fair; time-traveling in the science fiction sense first recorded 1895 in H.G. Wells' "The Time Machine." To do time "serve a prison sentence" is from 1865. Time frame is attested by 1964; time line (also timeline) by 1890; time-limit is from 1880. About time, ironically for "long past due time," is recorded from 1920. Behind the times "old-fashioned" is recorded from 1846, first attested in Dickens.