1. Datacenters or datacenter construction may be the most high-tech ones I would try. Not cloud services, but the literal physical buildings.
2. Musical instruments, art supplies, or other cultural/religious goods of some kind, possibly as high-tech as electric guitars or synthesizers (although those have not historically gone well).
3. Financialization businesses like insurance or securities packaging of some kind could work (if you don't get high on your own supply).
4. Food and hospitality never go out of style.
I assume that the way this sort of business would work is a 3-step process:
1. Start by becoming the best in the world at something very weird and specific.
2. Bootstrap your business with enough connections to start making sales without needing significant financing. Run as a completely bootstrapped business.
3. Convince your children to continue being the best in the world at that thing and maintain your values. If you don't have any suitable children, adopt one. Also, make sure to disinherit any children who are not both very competent and fully onboard with the plan - you need to keep the power concentrated in the one or two best successors.
It's no accident that a lot of these long-lived businesses in Japan, where all three of these are part of the culture.
One answer would be focusing on basic human activities. People will still probably be eating and traveling in 500 years.
Another would be to figure out and/or develop the “temple” of whatever future belief system or religion one thinks will be necessary and popular in the future. And this could be a currently existing religion; Islam and Christianity will probably be around in some form or another for a long long time.
With wooden furniture you are (at least for some time) also blocking release of stored CO2 back into atmosphere, a fate all other wood faces.