What is the oldest known prediction of constellation positions? Would someone know of a good reference on the oldest known predictions of constellation positions?  

How far ahead could accurate positions be predicted? 

For example, could current constellation positions be accurately predicted between A.D. 69 to A.D. 86?
No, there is no possible way that humans from any known civilization in the first century AD would have been able to extrapolate current constellation positions.

Prior to the work of Johannes Kepler and Isaac Newton, humans did not have sufficient knowledge of the basic principles of celestial movement to have any kind of basis for making such calculations.

Second, even if they had the basic principles, they would also have needed much more accurate and detailed information about the makeup of the Milky Way galaxy. The information currently available, that goes into the NASA models, is the product of a great many man-years invested in both observations and analysis of those observations.

Third, even if they had the basic principles and the necessary details with which to create a proper model, they lacked the computing power necessary to actually run the model - computation of that time being limited to pencil and paper (or perhaps an abacus).