I agree, the key with Green Cheeks is to not let them win! I know it's difficult to totally ignore it when she bites you, but you cannot hesitate or stop the motion of putting her inside of the cage once you start, because every time you do that she is learning more and more that if she bites you, she won't have to go in her cage.
So, always have her favorite treat inside of your pocket before you go to put her back inside her cage. Then when it's time to put her back in her cage, you need to tell her that it is time, by choosing a phrase that you will say every single time you start to put her back in the cage, so that she knows it's time; something like "Time to go home!" or "Time to go in your cage!", etc. So you just get her to step-up onto your finger, then say the phrase (and say it happily and excitedly, not in a firm or negative tone), and give her a treat or a piece of the treat right after you say the phrase. Right after you give her the treat or piece of the treat, start taking her over to her cage, and put her inside, totally ignoring any bites you might get...However, the idea is that she won't be able to bite you because she'll have the treat in her beak...So you get her to step-up onto your finger, say the phrase, give her the treat, then take her to her cage and put her right inside onto a perch. Then once she's off of your finger and inside the cage, you praise her excitedly and happily. Then you shut the cage door, and once she's finished the first piece of treat that you gave her, then give her the rest of the treat or another whole treat (depends on what it is, if it's something like a raw sunflower seed or a pine nut then just give her one after she steps-up onto your finger and you say "Time to go in your cage!", then another one after she's sitting inside the cage and you've said "Good Girl!"). Then shut the cage door, and I'd hand her another treat through the cage bars, again praising her. And if you follow this every time you take her to her cage, she'll get it down within a short amount of time...And again, the idea here is that she won't be able to bite/nip you as you're actually putting her inside of the cage, because if she does she'll have to drop the treat...If she does drop the treat and bites you when you're putting her inside of the cage, then you don't want to scold her for doing it, because this will give her mixed signals about going into her cage. Instead, you just completely ignore the bite, as if it never happened, just shut the cage door and then again give her another treat and praise her, because she's inside the cage. She should get the idea within a very short amount of time this way...
***Also, I highly advise you to NOT USE A PERCH/DOWEL to put her inside of her cage. This isn't a good idea for a number of different reasons, but to make it simple, you want her to step-up onto your finger without any issues, which she apparently already does, so you don't want to introduce a perch/dowel for that purpose...This is sometimes unavoidable with larger parrots, such as Cockatoos, Macaws, Greys, etc. who can bite a finger right off, but with a hand-tame Green Cheek Conure who is just being stubborn and nippy, their bite/nips are not anything that can't be taken and ignored.