Can't figure out how to make a tapered symmetrical open donut

I'm trying to find a way to make something like the attached image. The closest I could get is the other attached image (basically a circle, revolved symetrically, with chamfered ends (I couldn't chamfer more than 0.9mm before it wouldn't work — why is that?). The profile should smoothly taper from the thickest, about 2mm at its center, to the thinnest, about 1.2mm at the tips. Thank you!