With that restriction, you're left with a combo spare-tire carrier/jerry can mount from Off-Road Fabricators. It does not use the bumper at all, it mounts to special hidden brackets that support its weight via the rear rollbar mount bases.
ORF Spare tire and Jerry-can holder
I had one on my '97 TJ that was stolen a few months ago and it worked so well over its 7-8 years that I installed the same carrier onto my '04 Rubicon last month. It was completely sag-free and rattle-free the entire time even though it was always loaded with two full five-gallon jerry cans and a heavy 35" tire.