Can you set rounded pixel corners in Photoshop?

I find your question quite interesting but I’m not sure what do you mean by it.
If you’re trying to make a round corner you can simply follow the tutorial (not for photoshop, but the same principles are applied) in here: http://www.subcide.com/articles/creating-rounded-corners-with-precision/

But if your aim is to have a single pixel with a felling of a rounded corner than it’s much more troublesome.
Pixels are always rectangles and we are able to create the illusion of a round corner because of a high pixel density on the screens (and a certain distance from the screen). Pixel art is saved with only a few pixels but usually is shown in a ‘zoon’ state where each pixel is displayed using many pixels (otherwise the would always look very small on modern screens).

If you want to give the illusion that a single pixel has round corner you will need to draw that corner with more pixels, that is ok because as said before you usually already display the pixel art with more pixels. You can do that by either having a bigger canvas where you’ll paint large rectangles in place of the ‘normal’ pixels and draw your round edged pixel where you’d like. Or you may draw your pixel art as a vetorial image where your 30×60 elements (pixels) will be rectangles and the one with round edge has the shape you desire.

A mixed approach where you draw your pixelated image and after that draw a a vetorial image of the round edge pixel over the desired position can also achieve the desired result.

Either way these may not be considered ‘true’ pixel art, but would at least have a pixelated style. You didn’t say what the image was for, but this should be ok in some applications.

Hope this is what you where looking for.