The term for the rounded sheetrock corners is 'bullnosed'.

Look at a millwork company(or two or three) catalogs(should be available on line) for bullnosed corners.

It is possible to make the corners, but that takes some woodshop tools like a miter saw and a table saw. The idea is to cut several pieces at angles to glue together to make a rounder corner.

If the base is to be painted, making corners is much easier, since any gaps can be filled, meaning the angles do not have to be perfect.

Then the outside faces are sanded rounded and smooth.

One other trick finish carpenters use is how to more invisibly join straight pieces along a wall run. Instead of just butting the two pieces against each other, a scarf joint is used---each piece is cut at matching 45 degree angles and glued together. When done correctly, the joint is often very difficult to see without paint/etc.

Painted or stained? What radius?

For a larger radius use 3 plies of 1/4" bending plywood ("wigglewood") laminated together following the curve. You can probably just glue and nail it in place without having to make a bending form.

You can do the same for stain, but you'll want to veneer it for the finished look, adding some complication, probably requiring either a form or a vacuum press. to apply the veneer.

If the curve is a small radius (less than a couple inches) then you can just cut a corner piece out of solid wood matching the curve, or miter several pieces together as suggested above and sand them to a smooth curve.

Find a molding supplier other than a big box. They generally offer a variety of shapes that can be ordered to fit any number of configurations.

We have some curves in our house and I was told by the hardwood sales people that moldings come in flexible materials for just such things.

trim carpenter.