Woibles

Picture a sphericon, [link], now cut away any excess meat until all that remains are the surfaces which contact the ground as it rolls and the middle bit holding it together.
This middle bit should be then shaped like a rounded thread spool.

Give the cut-away spericon shape a mental push and you can see that there is an opening running horizontally through the off-set center of the rolling shape. In other words you can hold a dowel through the middle of this shape and not touch the sides as it rolls.

Bend that dowel, weight its ends and let it ride atop the thread-spool on a curved bearing with a gimbaled u-joint which allows the spericon to roll beneath it while the ends of the dowel stick out of either side like a tightrope walkers’ pole.
From these two weighted ends rigidly attach two more dowels bent up and over the rolling shape. They will not interfere with movement and will remain an upright support from which to suspend an inverted egg-shell shape from the shells' inner apex.

We now have a weeble bobble-head that will appear to walk down very slight inclines with a rhythmic swaying gait.
Conversely, (this part is just speculation) tipping the weeble in any direction should start it walking on its own until the pendulum motion is depleted.
Perhaps even 'up' slight inclines.