When was a daisy air rifle model no 1201 reg no F251882 made?

I can not give you an exact date, but here is what I have found. My catalogues do not list the model 1201 but they do list the model 1200 made (1976-1977) and the model 1205 made (1979 -1981) the model 1205 was an economy version of the 1200. I can only guess that your fell somewhere in the time frame.