I just adopted a sun conure from an elderly woman who raised him from 3 1/2 weeks old...he has been with me for 8 days today and will be 3 years old on May 1st...as I type this, he has burrowed down into my shirt, turned around so his head is facing my neck, is laying on my chest completely covered up, clearly nearly asleep, occasionally grinding his beak.
I feel your pain!! I've had my white eared conure for over a year now, and before I moved into my apartment from my parents she lived with a friend of mine(For just a couple weeks, issues at home, dad threatened to put her outside. So she moved out before me, just in case.) who absolutely adored her, so she had free range of his apartment while he was home. He told me about how she would lay down on her back and sleep on his chest, and I had to try so hard not to explode with jealousy... haha. But I know she loves me, even though I wish someday she'll nap on her back with me...