This sounds like an overbonding issue.
Conures are pair bond birds, like macaws and amazons. In the wild, even though they live in a large flock, they pair up, and they mate for life, and become almost inseparable.
In captivity, they have a tendency to form that same pair bond with a favorite person. If they are allowed to over bond, then anyone other than the favorite person trying to handle them will get bit...
The favorite person gets bit, when that person pays too much attention to another person. It's a jealousy thing... Like, suppose your husband is flirting with another woman right in front of you. You'd get mad, right?!
Same deal.
This is a socialization issue. He needs to be handled by more people. Basic biting and step up training with strangers. And you need to be out of the room when that happens, because they get bit the minute this bird sees you...
Enter the room unannounced, same deal.