Emirates received its first A310-300 in 1987. The aircraft, A6-EKA, was a brand plane directly purchased from Airbus.
Incidentally, A6-EKA was retired from the fleet in Q298 and sold to Royal Air of Canada (via Airbus). Don't know where it is now.
Emirates are replacing the A300/310 fleet with the A330s. This is probably because the A330 is bigger (both pax and cargo capacity), more efficient to operate, and newer (featuring nicer cabin and IFE).
Also the A300/A310 have basically been depreciated. EK's policy is to typically operate aircraft for 10-15 years, but during that period, work them hard. Then they sell them.