I'm happy to be corrected on the below, but I believe at this moment in time and taking one type from each contending airline, they may be as follows:
In 3rd place is British Airways and their two remaing first batch of B747-400s, with G-BNLN having a first Flight 17th July 1990 - 28 years 6 months

In second place, Lufthansa and their early Airbus A320-200s, with D-AIPA having a first flight date of 2nd August 1989 - 29 years 6 months

In 1st place, Air Canada and their remaining Boeing 767-300 fleet, with C-FCAE having a first flight date of 22nd April 1988 - 30 years 9 months

If I've overlooked any I would be interested to know.
Neil