So I am attempting to make a computer desk tray, and make a coster size hole without going all the way thru for my glass to sit in.
Circle is about 3 inches in diameter and 1/8 inch depth .
You can engrave a depression. Use a filled circle to represent the engrave.
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Depth of the engrave will depend on material and power/speed settings. Pretty much trial and error. Might require multiple passes.
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I use the concept frequently, You will discover that any wood grain will be accentuated in the bottom…
it will be difficult to sand flat and keep the sharp edge at the sides’
If the design can stand it a hole all the way through and then a smooth piece of wood underneath or even wood with a cork facing could be useful. or conversely a ring of the 3-inch inner diameter and sanded outer diameter to give a crater like result
For my own drink holders I use tapered capped containers and open holes to limit the possibility of spilling onto the keyboard 
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