Goliaths are basically where the principle of having all creatures be medium or small thematically breaks down. People play them because they want to play a really big character, often as much for RP as any mechanical advantage, but WotC didn't really give them any mechanical support for their prodigious size beyond the common and boring "Powerful Build".
I love stones endurance; "you hit me, but your puny weapons are no match for Goliath skin" is badass, and just saying you can use it once per minute, or your constitution modifier number of times, or three times per short rest, or whatever would probably be enough to make the Goliath more mechanically competitive. But I think what I'd really like is something that played on their size. It's a shame perhaps that Bugbears snagged the extra reach as that would work well. Perhaps something with an extra d4 of melee damage in keeping with the enlarge/ reduce spell's approach to size. Presumably this would require being limited use because, while I'm not sure an extra 2.5 damage on average would really be as powerful as it might seem at first blush, the DPR fixations of the powergamer would make it seem way to powerful in the popular imagination.
I'd also just consider making them count as a large creature for some purposes. This obviously changes their relationship to a lot of game mechanics though. It would be an interesting experiment for a player and DM who were both onboard.