This is a scroll saw method but I assume you can do the inlay thing other ways as well. The whole process took less than an hour not counting the glue-ups. Do the inlay on the top piece only.
If you want to do an inlay on a curved medium like a chair back first make up some home made veneer about 1/8 thick slightly larger than the finished piece.
Make a small piece of dark wood 1/8 thick slightly larger than the inlay.
Stick the pattern on the dark wood with spray on contact cement and stick it to the top layer in the proper position with double sideded tape.
Set your scroll saw table at about 8 degrees left tilt and cut clockwise around the pattern. This will create a tapered inlay that will fit tightly into the hole created.
Lower the dark wood into the resulting hole with glue and press it flat for an hour.
Laminate the remaining pieces on the curved mold and voila.
P.S. Your table setting will vary depending on the thickness of the inlay and the size of the scroll saw blade. Test on scraps until you get the right taper for a perfect fit.