Round Inset is a handy tool for Inset face with 100% original round corners. You can define the corners to be kept by setting a threshold value (on the Left-bottom menu). The tool will inset the face with original corner shapes. You can also use the Scaling setting to fine-tune the result. It can then use bevel to create nice round surface.

Prevent Overlapping:
Another important ability of this tool is creating inset without corners overlapping. It works for any faces. For faces without round corners, just use the tool and set the "Threshold" parameter to zero.

Update
Version 2.1.1
Fixed a mistake for installation

Version 2.1.0
Added the Merge option for merging collapsed vertices

Version 2.0.0, 2.0.1
Added "Prevent overlap" option! It will try to protect the corners from overlapping.
This feature works for "normal" face too (faces without any "round corner").

Version 1.1.0
Added scaling option for corners. Now you can change the shape of corners easily.