No, gold is one of UPS’s prohibited items. If you would like to ship gold, the safest and only way to do it is by Registered Mail with the USPS. I’ve delivered a few gold bars myself in my time there.
This way, your package is insured for up to 25,000 dollars if you choose to go up to that level. Which gold could easily hit. There is also the additional safety feature of registered mail which means every single person who received your package throughout its journey had to sign for it.