First of all, yes, MOST Conures do love to lay on their backs, as they are little clowns, and they often show-off by rolling-over on their backs, or they do it while playing, or they sleep on their backs. My Green Cheek, Bowie, loves to sleep on his back in his hammock and while snuggling against my neck, and I taught him "Play Dead" where he'll roll onto his back in my hand and go limp, lol...I've actually seen some of the young Green Cheeks in Petco come up to the front glass, trying to get my attention while I'm buying pellets and seed across the aisle, and they'll roll onto their backs with their feet in the air, showing-off and saying "take me home with you!"
That being said, each bird is an individual, and not every Conure will like to be on their back, it's just how it is...
However, if I were you, before I worried about teaching your Conure any "tricks" or anything like rolling onto his back, I'd be much more concerned with building a bond with him and hand-taming him so that he can be handled and will readily step-up for you, fly to you, let you pet him, etc. That's far more important that trying to teach him tricks like this, and not only is it more important, it's going to be extremely difficult to train your bird to do anything at all because you haven't yet earned his trust....Once you earn your bird's trust and he'll step-up for you and you're able to hold him and pet him, he'll be much more willing to listen to you and pay attention to what you're telling him to do or trying to show him. Right now if you try to start teaching him tricks, he's going to be anxious and far more concerned with what you're hands are doing, where your hands are, if they're getting close to him, etc. So I'd start working with him every day on hand-taming/trust-building, and once that comes then you can start teaching him to do tricks, and it will be much easier...