Before I write this I have to say, I don't encourage anybody to keep these rays and I don't consider myself an expert by any means. So, I've only ever acquired 4 of these rays and I've kept all of them longer than most seem to be able to (which could just be good luck).
I think one of the most important things is to find a ray that isn't too far gone. A lot of rays have already sat at an LFS just starving without anybody taking the time to get them to eat. Any ray that is withdrawn and super skinny looking probably aren't going to make it. I always look at the base of the tail. If it's sunken in and you can see the two bumps on the side of the tail REALLY protruding, then that's a ray I wouldn't touch.
If you find a ray that still has some girth to it, you should try to get it to eat right away (if you can buy one that's already eating, that's great). I always start with live ghost shrimp. I use tongs to get the shrimp right next to the ray. I've found that they almost always eat these. Once they're eating ghost shrimp, I've found their favorite food is squid. The next step I take is cutting the squid in SMALL pieces (about a 1/4" square) and burying it in the sand next to where the ray likes to hang out. They usually find the squid in the sand and at least pick it up and spit it out a few times before eating it (if they pick it up and don't eat it, I try again with garlic soaked squid. This has always enticed them to eat for me). Once they start eating, I haven't had any problems varying the diet and getting them to eat by hand. Mine are pigs and always swim to the top of the tank to be fed and splash water everywhere.
I also feed frequently. At least once every day, preferably twice. Other than that, my theory is that you need pristine water quality and the water should have a high oxygen content (I run an air pump in my sump). Again, I don't know if there's any merit to this, it's just what I do.
I must say again, I'm no expert and I don't want people to purchase these rays based on what has worked for me. I'm sure other people have had success with these rays using entirely different methods. I might have just had really good luck with the ones I've gotten. Wow, that was the longest post I've ever made on this site.
Whoops, the bigger one is about 9" across and the smaller one is about 6.5".