There are some silent ones, since they are passively cooled GPU's in the 7750 & 7770 series I believe. So without the fan it would be silent, but obviously the heatsink is huge for the GPU and of course it's not that powerful.
Otherwise you can go with Watercooling and go over the top on radiators and use really quiet fans and/or a fan controller to reduce the noise of them.
Water cooling is probably the best option, it's just more expensive, but means you can go for bigger cards yet still achieve silent operations if you get your setup right.
Water cooling is always the way to go if you need things totally silent. I water cool my CPU but just because they make easy to install kits for it that cost very little. But for the lower end GPUs (sub 7950) its just not necessary. 80C is a perfectly fine running temperature for a GPU and most stock heat sinks can do that no problem. The only reason for wanting to water cool a GPU is if you want complete silence and they run like $100 each just for the waterblock