NJS,
No worries, I've been busy with a plasma build. As Boswell mentioned, knowing what CAD software you're using would help. In Fusion 360 I would just sketch a circle of the large butt diameter, then extrude the length and set the extrusion taper angle - one shot and done.
Or you could create a sketch circle, then an offset plane the length of the butt with a smaller circle sketched concentric with the first. Select the first circle and 'loft' a body to the second circle. Two steps and done, but you don't need to know the angle - just the length and two diameters.
And the key point is that if you don't have a 4th axis and the capability of continuous cue rotation then the small diameter of the cue will be a problem. If you model the diamond as a flat plane then just extrude down the center of the feature will be deeper than the edges.
What you need to do is project the diamond on to the curved surface and then extrude (or whatever the CAD term is) down from the projected surface so that the depth is the same across the feature. The bottom of the diamond 'pocket' should have a curvature that matches the cue (smaller radius, however).
Then the CAM should be able to do a 3D contour operation that follows the curve and cuts the material.
Your other problem is that the outer edges will not be cut perpendicular to the surface, even with the 3D tool path. The edges will be slightly undercut because the tool stays at 90 to the center, but as it moves away from the center and moves down in Z the angle changes in relation to the outer (uncut) surface. The wider the diamond is in relation to the cue diameter, the more pronounced this will be.
Not a big deal if you're filling with epoxy, but if you are cutting wood veneer to inlay it might need quite a bit of hand-fiddling to get it in with tight edges.
And if you plan to turn it by hand, you might use your lathe to build some sort of indexing fixture. If you get the cutting sorted, look in to getting a cheap 4th axis off e-bay to use as an indexer. I wouldn't trust it for continuous cutting as there's going to be tons of backlash, but as an indexer it should be OK if you only rotate in one direction. That would open the possibility to multiple patterns on the cue as you work your way down the handle (4 big diamonds, then 6 small, etc.). The cheap belt or gear-head ones driven by a stepper should be pretty cheap to integrate. I wouldn't even post the Gcode with 4th axis moves - just run one diamond and then jog the 4th by hand to get to the next point.
Good luck. Keep us updated.