Not sure. I think you can probably use C14 dating to get an approximate age, within a couple of decades (this assumes natural occurrence, not post testing). I’m having trouble finding information about accuracy of carbon dating for young samples. Surely precision for younger wines (say the 20th century) can’t be anywhere near 1 year.
You’re right that the precision can’t be anywhere near 1 year, except for wines in the era affected by atmospheric test-produced 14C. The half-life of 14C is around 5600 years, so you can’t get that level of precision from following the radioactive decay even if there weren’t other problems. But after the peak of the bomb pulse, you can get something like that precision (as authors have quoted). The atmospheric testing roughly doubled the amount of 14C in the atmosphere. But this extra 14C is equilibrating with the biosphere and ocean by the various processes in the carbon cycle, ie the extra contribution to the atmospheric abundance is disappearing much more rapidly than the radioactive decay rate (note that by 2010, roughly 90% of it is gone). That much faster decay rate is what allows a much greater precision for carbon dating in this period.
As far as accuracy of dating samples in the “modern” era but before 1950, it’s related to the calibration curve. If the C14 fraction in the atmosphere were constant, carbon dating would be straightforward. But it hasn’t been constant, so the methodology is to calculate a raw 14C age, typically expressed in years BP (“before present” or “before physics”, defined to be before 1950). A lot of effort has been put into using tree rings and other things to construct a calibration curve to convert the raw age to a calibrated age. A link near the top of the page at http://www.radiocarbon.org/IntCal04.htm gives you the IntCal04 2004 compilation of this calibration curve. If you look at the last plot in that link, it shows the calibration curve in the recent past with raw 14C age BP on the vertical axis, and calibrated age BP on the horizontal (with a one sigma uncertainly envelope). If you look down in the lower right, you’ll see that variations in the atmospheric 14C have caused the conversion between raw 14C age and calibrated age to become multivalued. When you consider the uncertainties shown in the calibration curve, you’ll see it’s basically not feasible to apply radio carbon dating to assign ages for the 250-300 years before 1950 (except with an error bar that spans that range).
-Al