Sorry for not getting back to you last night, but sleep overcame me. Here is a example of one way to do a rocking chair. You will need to loose the ".TXT" part of the file extension before you can use the zip.

This rocking chair prop should work for at least P4 and above. There is a dial named "ROCK" to implement the rocking motion, this is just a dial name slapped on to the xRotate channel. Another dial "Ratio_A" lets you set the ratio of zTran to xRotate. The default ratio of 0.444 is probably not correct, but I could not be bothered to get it exactly right.

Here is the relevant coding:

        valueParm Ratio_A
            {
            name Ratio_A
            initValue 0.445
            hidden 0
            enabled 1
            forceLimits 0
            min -100000
            max 100000
            trackingScale 0.001
            keys
                {
                static  1
                k  0  0.445
                }
            interpStyleLocked 0
            staticValue 0.445
            }

        valueParm TranMaster
            {
            name TranMaster
            initValue 0
            hidden 1
            enabled 1
            forceLimits 0
            min -100000
            max 100000
            trackingScale 0.1
            keys
                {
                static  0
                k  0  0
                }
            interpStyleLocked 0

            valueOpDeltaAdd
                NO_FIG
                RockingChair
                xRotate
            deltaAddDelta 0.010000

            valueOpTimes
                NO_FIG
                RockingChair
                Ratio_A
            }

The two valueParm channels above have been added to the top of the channel stack.  The value in the Ratio_A channel, "0.445" in the above example, is to be determined experimentally, or mathamatically based on Pi.
The zTran channel (below) has had slaving code added (showen in green).

        translateZ zTran
            {
            name ztran
            initValue 0
            hidden 0
            enabled 1
            forceLimits 0
            min -100000
            max 100000
            trackingScale 0.001
            keys
                {
                static  0
                k  0  0
                }
            interpStyleLocked 0

            valueOpDeltaAdd
                NO_FIG
                RockingChair
                TranMaster
            deltaAddDelta 1.000000

            trackingScaleMult 1.000000
            }

The "#" is just to mark interesting places in the file.

In this prop, the origin has been set at the center of the circle formed by the arc of the rails. The motion of the chair is corrected by using zTran. This is probably the simplest way to do the slaving.

I might get round to doing another version with the origin at the bottom of the chair and using yTran to correct the motion.