You’ll need a power director that turns on the outlets with a 12-volt trigger. Panamax and Monster make some (the former will probably be much cheaper).
Alternately, if your receiver has a switched convenience outlet on the back, you can get a vintage Adcom ACE-515 on ebay, typically for under $75. Cool thing about it is will delay on and off for the amp, which can avoid a "pop" in the sub when powering up the system.
Here is a close up view of the slave/master power strip. Master would be to the right out of picture. When you use your AVR you just plug into Master. Then all the slave switched will power on when the AVR is turned on. When the AVR is turned off the AVR will go to standby like normal and the salve points will turn off the power completely.
That is one option or you can build a relay box yourself. For just powering on one amp I would use the power strip. Thats how I am turning on my subwoofer amp. But my amp can turn off power or turn on power silently. Not sure the Berry does that or not.
I am wondering if there would not be a better way to auto power on/off by tying into the actual power switch on the Inuke. So that rather than power being connected or disconnected at the outlet, that it would actually get switched on and off at the same location as the physical on/off switch. Maybe this would be better than what is effectively plugging and unplugging the unit while power up? I would think that it would eliminate the power thump.
If the iNuke is like most devices with a hard power switch, the hot lead from the power cable goes first to a fuse, and from there directly to the power switch. I.e., the power switch switches only the hot lead, not the common and ground. Any power management device (e.g. from Adcom, Panamax or Monster etc.) does the same thing, switching only the hot leg. So they aren’t “effectively plugging and unplugging the unit.” Thus, most likely tapping directly into the iNukes power switch won’t make a difference.
Now, if your personal experience shows that the iNuke does not have a thump when manually turning it off and on, then it might be a worthwhile endeavor...