Not into stuff like that myself but I would have thought the purpose of nipple rings was to show that you have nipple rings. Put on a tight shirt and walk proudly through the library with your chest out like a proud pigeon kind of thing.
But I guess one solution is to get extra piercings on your chest and stomach so people won't be able to tell which piercing is the actual nipple piercing.
I want to get nipple piercings because I want anybody who have sex with me to play with them and, as a bonus, humiliate me and degrade me. (yes, I know, body modifiers frown upon the sexualization of piercings, but I want them precisely because they are sexual, lol)
But I don't want Karen, Christian Mother of the Street, to be denouncing me to the police for being a gay freak of nature who will transmit homosexuality to her children when they see my piercings through my shirt.
I had a friend who was very self-conscious about her nipples. She used to wear band-aids over them whenever she was wearing a tee shirt or something that might let them show through or even just poke out a bit.
You can get them in various sizes, and as far as I know they stay on pretty much all day. If you have chest hair, maybe look for something a bit less aggressive when it comes to removing them.