Here's few questions for you before I go on:
-Do you cover the cage when putting to bed? Even a dim light can bother them. Mine will complain and crawl around the cage unless I cover him, despite there are the dimmest corner light in the huge room.
-does he have a sleeping spot? Conures in the wild usually sleep snuggled and huddled up against each other. To mimic this, a tube/see through seagrass tent can give them this feeling, and most will sleep there. Or huddled against a toy while perched.
-Any noise could keep your bird awake, especially things like watching movies or listening to music. Especially if it's not pitch dark for them.
-How old is the bird?
Mine also never naps during day, rarely rests. Mine has a bed time straight from 10pm till 9am (I work from home). Before his actual bedtime we have more or less dim lights in the room starting from the evening, so the birds has lots of time to adjust for the sleep time. The lights go off automatically at 10pm, so birds tuck them selves away immediately when only light is on is the corner light just so I can navigate around the room. We almost never use ceiling strong lights in the late evening. Neither should a human go suddenly from bright light to a pitch dark - it's really hard to go to sleep like that!
When I got mine, he would get up with the sun and go to sleep with the sun, it was spring so he'd already be sleeping at 6-7pm and be awake at 5am, but not shouting.
Also it is possible the bird simply wants to be with you. Try using words like "night night" or "sleeping we go, see you in the morning" or anything you choose. Bird should by time learn the meaning behind it. 2--3 weeks seems like a good period for a bird to adjust to a sleeping regime, I know mine did. Because at home we have such a strict regime when it's bed time for the birds, he will start complaining and shouting like 10 minutes before the lights go off, if I am not in the room. He knows I should cover him, and he reminds me to stick around just to cover him once the lights go off.