Solid modeling:

I tried taped extrusions in AutoCAD 2002 and it failed to work on elipses
Im not sure if this was remedied in later versions, I do know that the default extrude command does not include a taper command in 2007.

You might not be able to do this using a true elipse
A collection of circles trimmed down to look like an elipse will still allow a tapered extrusion but the model wont be 100% accurate anymore

Surface modeling:

With your upper and lower elipses already made you can do a ruled egde to get the angled sides. A simple region/face would make the top/bottom

The downside to this method is you cannot modify the shape further

Lisp:

Mesh to solid on a ruled edge will make a good rough model that is highly dependent on your surface tabulation values. Since ruled edge only makes flat faces - alot of them - you wont get a true eliptical curvature from it

The plus side is you can manipulate it further