Use some epoxy or some sort of cement. You’ll want to mark the rings with a pen(whiteboard marker works good for temporary markings) so you can line them up for replacement. Mark at least 2 spots and don’t mark both halves the same so you can clearly put them back where they came from.
The idea is to see if you can pop the rings off completely, use the glue or cement sparingly, and then press the ring back on and line them up immediately. Remove the axle from it and let it cure over-night. Place the yoyo rim down and weigh it down with a heavy book(dictionaries work best).
If you can’t remove the rings, use a glue with the finest application tip you can find.
You may find simply pressing the rings back in place really hard will be sufficient. I’ve had this happen to my Speeder 2.
Nope nope nope nope nope nope nope. The rings of an Atmosphere are supposed to come off. And rubber cement won’t work since nothing will stick to celcon plastic, that is why the rings are press fitted instead of glued in. A change in climate or heat can cause the plastic to expand letting the weight rings wiggle out.
This is bound to happen when you connect metal and plastic on a yoyo, impacts, climate change, there’s a lot of reasons why this would happen. Even simply unscrewing the yoyo to many times can loosen the rings.
I seem to remember a thread on YoYoNation a couple of ears ago by IV relating to this. He fixed his Atmosphere by heating it up in hot water (to soften the plastic slightly) and then pressing each half down on a table to seat the rims.