Update-
While the initial design did do the job once set up properly, it had its drawbacks. Namely, it required way too many pieces to hold the servo in the right position, and even then it required constant adjustment to get the proper motion.
A much better approach was suggested to me by a friend who had a baby the same week as I did... Instead of attaching the rocker to a chord controlled by an exterior-mounted servo, he suggested mounting a continuous rotation servo on the rocker itself with either a cam shape, or single arm propelling the rocker forward on each rotation.
I can post photos later, but the result is a much simpler setup with a far more consistent motion. There is one significant drawback however... With the first setup, the sound of the back and forth motion created just the right amount of white noise to put my son to sleep. The continuous rotation servo OTOH emanates a high pitched whine of the type that signals distress or strain in both the animal and mechanical world alike! As for my purposes, the continuous rotation servo is really just a geared dc motor in a hobby form factor, I wonder if I could replace it with a different motor that would produce less noise? Or at least, one that doesn't sound so grating?